Conference Agenda

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Session Overview
Location: 301B
Oral Session
Date: Monday, 20/June/2022
10:00am - 12:00pmPower Electronics
Location: 301B
Session Chair: Katie Sheets, AFRL
10:00am - 10:20am
Power Electronics: 1

A new topology for DC-DC converter with enhanced current multiplication

O. Zucker, T. Le

Polarix Corporation

Electronic DC to DC converters[1] divide into those that use transformers[2] for impedance transformation and those that use resonant transfer between capacitors and inductors. In the latter, an inductance is used as intermediate storage that is energized at one voltage and deenergized at another. Some circuits combine the two approaches in one circuit such as opening a current carrying primary of a transformer. In general, the resonant transfer type such as the buck or buck boost circuits come in several basic variations and are inherently limited in their impedance transformation. For higher transformation ratios multiple stages are used which reduce the efficiency of the total system.

A circuit termed the “Meatgrinder”[3] was developed in the 1980s to enhance the energy transfer between an energy storage inductor and an uncoupled inductive load by breaking the energy storage inductor into coupled sections interspersed with intermediate switches and a prescribed sequential switching scheme. The arrangement increased the total energy transfer efficiency with the number of sections. Significantly, a variation of this circuit termed the “Ringer” and developed principally for energizing electromagnetic guns which used only two sections; and furthermore, used the ringing of the source capacitor to perform the opening switch function and thereby eliminating the opening switch altogether. This Ringer circuit has now been modified to energize various PWM inverters for motor control and related. Applications with substantially increased impedance transformation and efficiency and with more relaxed switching requirement.

Converter switch requirements include both opening and closing switches. Opening switches are affected by the ever-present leakage inductance whose inductive kick must be suppressed with capacitors and resistors to protect the switch from over voltage surges. Alternative approaches are to open the switch only when the current is zero. This often goes counter to the function we would like the switch to perform. the circuit described in this paper combines the switch opening of the inductive circuit with both enhanced current multiplication and efficiency and substantially reduced switch requirement.

The circuit perceived application is predominantly in compact high efficiency converters requiring large impedance ratio transformations.

[1] B. W. Williams, "Basic DC-to-DC Converters," IEEE Trans. Power Electron., vol. 23, no. 1, pp. 387,401, Jan. 2008.

[2] Hua, G., Leu, C.S., Jiang, Y., et al.: ‘Novel zero-voltage-transition PWM converters’, IEEE Trans. Power Electron., 1994, 9, (2), pp. 213–219

[3] O. Zucker, J. Wyatt and K. Lindner, "The meat grinder: Theoretical and practical limitations," in IEEE Transactions on Magnetics, vol. 20, no. 2, pp. 391-394, March 1984, doi: 10.1109/TMAG.1984.1063078.

10:20am - 10:40am
Power Electronics: 2

In-depth Analysis of current-fed resonant Full-bridge Converter Application for high voltage DC Power Supply

R. Grinberg1, A. Reichert2

1Bern University of Applied Sciences, Switzerland; 2Industrial X-Ray, Comet AG, Switzerland

In-depth analysis of current-fed resonant full-bridge converter application for high voltage DC power supply


In [1], current –fed full-bridge converter with resonant switching and constant on-time control for high–voltage (HV) application is introduced and demonstrated on 1kV/600W prototype converter with single rectifier output stage. While taking into account major parasitic components of HV transformer, theoretical analysis and demonstrator design in [1] does not cover the following aspects:

- influence of multistage multiplier and its component characteristics on converter performance and design for high output voltages e.g. 100kV

- impact of current-source implementation on the overall converter characteristics

- sensitivity of converter design to variation and uncertainties of HV transformer model parameters

- implementation aspects of current-fed converter.


This paper provides in-depth analysis of the aspects listed above. Using analytical and simulation approach, non-negligible effect of the multistage multiplier on the converter design is shown. Specifically, presence of significant HV diode junction capacitance leads to reduction of converter operating range. It is also shown that, in case of thin winding wire and multiple insulation mediums in the winding, analytical approach for HV-transformer capacitance calculation [2] does not provide estimates that are accurate enough. As an alternative, measurement-based approach, introduced and tested for two-winding transformers in [3], is pursued for parasitic parameter extraction and associated challenges are shown. Design trade-offs for current source implementation (in this case, buck converter) vs full-bridge converter on-time selection are shown. Specifically, it is demonstrated that time shift between constant on-time of full-bridge converter and buck converter significantly impacts current source output ripple and must be considered during the design. Finally, selected simulation results are compared with measurements on oil-insulated 150kV/300W high-voltage power supply prototype, discrepancies discussed and opportunities for future work identified.


[1] R.Y. Chen ; R.L. Lin ; T.J. Liang ; J.F. Chen ; K.C. Tseng, “Current-fed full-bridge boost converter with zero current switching for high voltage applications” in IEEE 2005 Industrial Applications Conference, 2005, pp.2000-2006

[2] L. Dalessandro ; F. Cavalcante ; J. Kolar, ”Self-Capacitance of High-Voltage Transformers”, in IEEE Transactions on Power Electronics, 2007, vol22, pp.2081-2092

[3] F. Blache ; J.P. Keradec ; B. Cogitore, “Stray capacitances of two winding transformers: equivalent circuit, measurements, calculation and lowering” in IEEE Industry Applications Society Annual Meeting, 1994, pp.1211-1217

10:40am - 11:00am
Power Electronics: 3

Study of a Medium Voltage AC/DC Testbed Employing Electrochemical Energy Storage and Power Electronic Regulation

A. N. Wetz1, D. A. Wetz1, J. M. Heinzel2

1University of Texas at Arlington (UTA), Electrical Engineering Department, 416 Yates Street, Rm. 518, Arlington, TX 76019 USA; 2Naval Surface Warfare Center – Philadelphia Division, 5001 S Broad St, Philadelphia, PA 19112 USA

Electrical power system architectures that are more intellingent are needed to meet the ever changing power requirements in both civilian and defense applications, respectively. Countless migrogrid topologies are being designed, modeled, and experimentally studied everyday to identify and hopefully overcome the many challenges that arise when distributed power sources and loads are interconnected and controlled autonomously. The Pulsed Power and Energy Laboratory (PPEL) at the University of Texas at Arlington (UTA) has developed a real-world testbed for the purpose of investigating control topologies that can be used to reliably control the power electronic distribution system when transient loads are sourced such that power quality is maintained. The testbed, operating at power levels in excess of 300 kW, utilizes distributed AC and DC power sources and loads operating at 480 VAC, 4160 VAC, 1 kVDC, 6 kVDC, and 12 kVDC, respectively. The testbed is being extended utilizing a hardware in the loop (HIL) simulator. The presentation will discuss the design of the testbed, the test plan methodology, and some results collected so far.

11:00am - 11:20am
Power Electronics: 4

Analysis of Resonant Behavior of Voltage Multiplier

A. Pokryvailo

Spellman High Voltage Electronics Corp., United States of America

By “resonant” behavior, in broad terms, we mean influence of the multiplier on the current waveforms of the HV transformer. The multiplier is seen by the transformer as an impedance, usually, a capacitive one. For a linearized circuitry, the multiplier can be substituted by a lumped capacitance, Cadd, connected to the transformer secondary terminals. Such an approach was actively investigated and formalized in the early years of Cockroft-Walton type multiplier developments. It is being equally actively and eagerly reinvented now, many decades later.

Parasitic capacitances Cp’s of the multiplier include geometrical capacitances, which are, in general, linear, and nonlinear capacitances of the semiconductors. Early researchers and those who followed them were fully aware of the complex nature of the parasitics. Schemes, of mostly inductive compensation, were suggested to alleviate Cp’s negative impact, including improved voltage sharing, or smaller “compression”, between the stages.

Usually, Cp’s are most prominent at no-load or at a light load. They were mostly how treated this way in the past. It was shown that even at no-load the output voltage would be lower than the expected 2NV0, where V0 is the peak transformer output voltage, and N is the number of cascades (for a classic CW multiplier). However, even under load, Cp’s are important, especially if the transformer is fed by a square- or other waveform containing higher harmonics. Cp’s are an unalienable part of the converter.

An interplay between the multiplier construction capacitances, Cm, and its Cp’s results in complex current waveforms. It is shown both theoretically and experimentally that at a low duty cycle, the transformer windings can be subjected to a “backlash” from the multiplier Cp’s, which generates spurious currents in the primary winding. Another non-trivial consequence is that with low Cm/Cp ratio, the leakage inductance is compensated more effectively, and higher power can be made, at a price of a larger compression. Yet another peculiarity is that even with very high Cm/Cp ratio, low Cm values result in the current waveforms that are more resonant, under heavy load, with N exceeding certain number of stages. This report concentrates on a classical CW multiplier. Special attention is given to analyzing compression caused by parasitics at no-load.

11:20am - 11:40am
Power Electronics: 5

Compact Magnetron Power Supply for Industrial Heating Applications

S. Wei, A. J. Watson, M. R. Ahmed, J. C. Clare

University of Nottingham, United Kingdom

This paper proposes a high-power Magnetron power supply for industrial heating applications with a rated power in excess of 120 kW and an operating voltage over 20 kV. With the aid of silicon carbide MOSFETs, the switching frequency of the power supply can reach 100 kHz, enabling a physical footprint reduction in which is advantageous in some target heating applications, such as those undertaken offshore. The converter modelling analysis and the combined voltage and current control methodology are presented. A non-linear Magnetron type load emulator circuit for the simulation work is also introduced.

The magnetron is an RF vacuum tube capable of generating microwaves. In industrial heating applications, the use of microwaves is much more efficient than traditional approaches using fossil fuels. One such application where the footprint of the heating system is critical is in offshore waste material treatment, where the cost of physical space is very high. Recent advances in the development of wide bandgap semiconductors and magnetic materials enable the potential for operating at a higher switching frequency potentially leading to a size reduction in the overall microwave generation system.

Due to the non-linearity of the magnetron load, a resistor is not sufficient to represent its characteristic in simulation environments, and hence an emulator circuit has been constructed. This provides a better approximation to the voltage-current curve for different working regions of the magnetron.

The proposed converter structure is a single active bridge (SAB). An AC input is rectified to produce a DC bus which forms the source of an H-Bridge circuit. This is connected to a high voltage transformer-rectifier unit (HVTRU) via an inductor for current control. The output of the transformer is then rectified and filtered before being connected to the anode and cathode of the Magnetron. Further details on the topology will be given in the final paper.

The SAB can operate under both continuous and discontinuous current conduction modes (CCM and DCM), and hence the transfer functions should be derived separately. Also, due to the requirement of the magnetron load, a voltage controller needs to be used when increasing the voltage before the tube conducts current and a current controller is required once the tube is conducting. Since the voltage controller works in DCM for start-up and the current controller works in both CCM and DCM, 3 different control approaches are required for the full operation of the system. The controllers are tuned to ensure that the output power of the RF tube can be controlled with an acceptable response and speed, limiting the possibility of arcs and being able to respond quickly to limit input power into the magnetron if one occurs, extending lifetime.

In the final paper, full details of the system design will be presented. The control design challenges and solutions will be presented and simulation results used to validate the operation of the power supply.

11:40am - 12:00pm
Power Electronics: 6

Impulse Generator for Simulating Lightning-Induced Pulse Transients for Airborne Equipment Test

S.-M. Park, W.-C. Jeong, H.-J. Ryoo

Chung-Ang University, Korea, Republic of (South Korea)

This paper deals with design and implementation of the test equipment capable of simulating various types of lightning-induced pulse transients required by an international standard which defines the test condition and procedures of airborne equipment. The impulse waveforms required by the standard are composed of dozens of types based on various criteria such as voltage and current level, shape, rising/falling time, and repetition rate. Therefore, existing commercialized test facilities use a method of charging a storage capacitor using high-voltage capacitor charging power supply (CCPS), and configuring PFN circuit with the capacitor to generate a required test waveform. However, according to various conditions as mentioned earlier, multiple PFN circuits are designed and the storage capacitors of each PFN have a wide capacitance range from several nF to hundreds of μF; so the CCPS is also manufactured in two or more units, and the method of selecting and replacing each CCPS and PFN according to the test condition is currently used. However, in this study, 11 PFN circuits for each waveform and a single high-voltage CCPS that can cover a wide range of load capacitances ranging from 1 nF to 150 μF with maximum ratings of 12 kV charging voltage, 20 kHz repetition rate, and 245 kW peak power were designed and developed. Since the CCPS should be able to charge the load capacitor with a relatively large capacitance in a short time while considering the precision of the charging voltage for the loads of several nF level, the proposed single CCPS is designed as a dual-converter configuration consisting of a high-power (HP) and low-power (LP) converter. Each converter is designed based on the modified LCC resonant converter for high-efficient operation, and is capable of being operated independently or in parallel depending on the type of test waveform. In addition, considering the required level and precision of charging voltage for each load, the HP converter is designed to automatically stop generating the gate signal when the charging voltage reaches approximately 7 kV. Finally, a single CCPS was developed in a volume of 29.3 L, with design considerations such as high voltage isolation and development of high voltage and high frequency transformers. Through the experiments using the developed CCPS and each PFN load, it was confirmed that all test waveforms defined in the standard could be generated.

Date: Tuesday, 21/June/2022
10:00am - 12:00pmSolid State Modulators
Location: 301B
Session Chair: James Randall Cooper, Cooper Consulting Services, Inc.
10:00am - 10:20am
Solid State Modulators: 1

Design and Analysis of a 24 kV PCB-Bus for the Low Impedance Interconnect of a Multiphase PEBB-based Converter

J. Stewart

Virginia Tech - Center for Power Electronics Systems, United States of America

In this work, the design and analysis of a medium voltage (MV) printed circuit board (PCB) -based planar power bus rated for 24 kV with distributed capacitor daughtercards is presented. This bus provides the low impedance interconnect between an external power supply input and two phase legs of a 24 kV/2 MW power electronics building block (PEBB) -based multilevel modular converter (MMC). The bus serves as a motherboard for capacitor daughtercards which are rated for 9 µF 3 kV each. Electric field (E-field) analysis and parasitic extraction was performed via finite element analysis (FEA) using COMSOL Multiphysics and Ansys Electromagnetics for board- and system-level integration. Insulation performance for each component and the assembly was verified through partial discharge (PD) analysis using an Omicron MPD600. The motherboard and capacitor daughtercards partial discharge inception voltage (PDIV) were tested on a layer-to-layer basis, in addition to the full assembly to ensure the system was PD free under normal operation.

A single PEBB is a converter in which the power stage and all ancillary circuitry required to operate independently are contained in a single structure. PEBBs may be stacked in a series and/or parallel fashion to achieve a higher voltage and/or current rating respectively. The 24 kV MMC includes four PEBBs in the upper arm and four PEBBs in the lower arm of each of the two phase legs. Each PEBB also has an independent forced air cooling system which is referenced to earth ground (GND). Due to the system’s complexity, the boards layer stackup and connector design were critical when fully integrated into the system.

This 24 kV bus was implemented using a 22-layer stackup with a staggered offset between conductor edges for field grading. A layer of FR4 with a controlled thickness was used between the outermost conductive layer and surface pads. This allowed high fields to be contained with the solid dielectric to avoid corona along the surface of the PCB. Additionally, guard pads were implemented to reduce the E-field intensity in air near terminals. These guard pads are placed directly below device terminals and connected to the same potential, at some height within the bus so the field intensity is reduced.

Eight capacitor daughtercards rated at 9 µF 3 kV each were mounted to the motherboard creating a 1.13 µF 24 kV capacitor bank. The daughtercards were constructed using a series-parallel array of 1.5 kV commercial-off-the-shelf (COTS) capacitors. Using this method, the target capacitance for our specific application was achievable. It was beneficial to avoid bulky high voltage can capacitors which require their cans to referenced somewhere near the voltage of their terminals. Additionally, the array of parallel film capacitors provided a much lower impedance which is desirable for such an interconnect.

The final manuscript will provide background on the 24 kV PEBB-based converter at the heart of this work. Detailed analysis for and design of the 24 kV PCB bus and the 3 kV capacitor daughtercards will be presented. Test methods and more extensive results will also be presented.

10:20am - 10:40am
Solid State Modulators: 2

A 30-kV Solid-State Impedance-Matched Marx Generator: Practical Considerations on Impedance Matching

T. Huiskamp, J. van Oorschot, M. Azizi

Eindhoven University of Technology, The Netherlands

Based on the topology of the Impedance-Matched Marx Generator (IMG) presented in 2017 by researchers from Sandia (and others) [1], we created a solid-state IMG using MOSFET switches [2]. The advantage of using the IMG topology is that by using transmission lines to transmit the pulses from the Marx stages the rise time of the pulses can be maintained at the output waveform (when carefully impedance-matched). By designing the Marx stages very compactly and using fast semiconductor components, adjustable pulses with rise times of just several nanoseconds are feasible with this topology. Since we require such fast rising pulses for transient plasma generation, the solid-state IMG is ideally suited for our purpose. In this contribution we present the development of a 30-kV version of the solid-state IMG. It utilizes 12 stages of gate-boosted [3] and series-connected 1200V SiC MOSFETs and achieves several ns rise time at 30-kV output voltage. Specifically, we also focus on the practical considerations on impedance matching with a modified, much longer version of the IMG to investigate practical considerations on impedance matching. We will show that if the matching criteria are not observed, severe distortion of the waveform is possible and that for the fastest pulses we need the best matching possible.

[1] W. A. Stygar et al., “Impedance-matched Marx generators,” Phys. Rev. Accel. Beams, vol. 20, 040402 (2017)

[2] T. Huiskamp and J. J. van Oorschot, “Fast Pulsed Power Generation with a Solid-State Impedance-Matched Marx Generator: Concept, Design and First Implementation”, IEEE T. Plasma Sci., vol. 47, 4350 - 4360 (2019)

[3] M Azizi, J. J. van Oorschot, T Huiskamp, “Ultrafast Switching of SiC MOSFETs for High-Voltage Pulsed-Power Circuits”, IEEE Transactions on Plasma Science, vol. 48, 4262 - 4272 (2020)

10:40am - 11:20am
Solid State Modulators: 3

The Stacked Multi-Level Klystron Modulators for the ESS Linac

C. Martins1, M. Collins2, M. Kalafatic1, L. Yury1

1European Spallation Source ERIC; 2Lund University Faculty of Engineering - LTH, IEA Division

The European Spallation Source (ESS) Linac will require by its completion a total of 33 klystron modulators. They are based on the novel Stacked Multi-Level topology and are rated at 115kV/4x25A; 3.5ms/14Hz, therefore capable of powering 4 klystrons rated at 1.6MWpk, 704MHz in parallel. Besides complying with the ESS requirements in terms of pulse quality (i.e. rise times0..99% < 120µs; flat-top droop <1%; ripple <0.2%pk-pk), they also comply with relevant power quality standards on the electrical grid (current THD below 5%, unitary power factor, flicker free operation), thanks to the adoption of Active Front End (AFE) rectifiers in conjunction with constant power regulated DC/DC capacitor chargers. These features allow their direct connection to the AC line without the need for external line compensators or filters.

The topology is modular and based on the association in series of 6 identical HV modules, each rated for 20kVpk and formed by a HVHF transformer, a HV diode rectifier bridge and a HV LC low-pass filter. These modules are placed in an oil tank and are driven by a 1kV/15kHz H-bridge inverter, which in turn is fed from a capacitor bank charged by the aforementioned AFE+DC/DC chargers.

The modulators have a footprint of 1.6m x 4m and a weight of 11.5 ton (including oil). The mechanical layout was designed in order to facilitate access to each component for repairing. In particular, the low voltage and high voltage cabinets can be assembled and repaired independently, with the first one directly pluggable into the top of the second one. The high voltage cabinet comprises the complete oil tank assembly and it can be easily extracted from each side of the modulator by using the built in sliding rail system, facilitating access for maintenance purposes and interchangeability of the HV modules.

In a first part of this contribution, an overview of the different blocks and functionalities of the power conversion structure will be addressed. In a second part, the main lessons learned during the design, construction and validation of both the reduced scale prototype and the full scale series units will be presented, together with the implemented corrective actions and their effectiveness. This will include issues related to the design of the HV modules like field control, effect of stray inductances and parasitic capacitances, integration into the oil tank, the reliability of the insulated oil and the impact of their handling procedures, the common mode noise effects and their mitigation, eddy currents mitigation etc. In the third part, experimental results obtained with the first 660kVA rated series modulator powering a HV resistive dummy load and klystron load will be presented and discussed.

A total of 18 series modulators have been delivered to ESS for the completion of phase I of the Linac construction, allowing an average beam power in the target of 2MW. For future power upgrades of the Linac to 5MW, additional 16 units of similar type will be required.

11:20am - 11:40am
Solid State Modulators: 4

Evaluation of Klystron Modulator Performance in Interleaved Pulsing Schemes for the ESS Neutrino Super Beam Project

M. Collins1,2, C. Martins1,2, M. Eshraqi2, B. Gålnander2

1Lund University; 2European Spallation Source ERIC

It has been proposed that the relatively low duty cycle of the European Spallation Source (ESS) linac allows acceleration of additional H- ion pulses interleaved with the baseline proton pulses, representing a unique opportunity to construct a neutrino super beam (ESSnuSB) facility of unparalleled luminosity. Coupled with a distant Cherenkov detector, it is believed that evidence of CP violations in leptons could be obtained, representing a significant step towards understanding the matter/antimatter asymmetry.

In this paper, several such interleaved pulsing schemes are considered from the perspective of the klystron modulators and the RF power system in investigating the possibility to realize the ESSnuSB. Conserving the required output RF energy, these pulsing schemes vary in terms of 1) number of added H- ion pulses per baseline cycle, 2) pulse amplitude and 3) pulse length. Each prospective pulsing scheme offers unique advantages while differently impacting klystron modulator performance. Whereas the ESS linac baseline design requires 33 klystron modulators (rated for pulse amplitude 115kV/4x25A, pulse length 3.5ms and pulse repetition rate 14Hz; each modulator powering 4 parallel klystrons rated 1.6MWpk at 704MHz), the proposed upgrade requires doubling the baseline linac average output power and thus either doubling the capacity of existing modulators or the procurement of additional modulator systems.

In order to evaluate and compare the merit of these solutions from a system perspective, a mathematical framework connecting the attributes of the proposed pulsing schemes to the power transfer curves of the klystrons and subsequently to the performance of the klystron modulators is developed. In particular, the impact on modulator-to-beam efficiency, modulator average input power quality, modulator output pulse flat top ripple, total upgrade cost, total operational cost (assuming a life time of 25 years), and required additional system size is assessed.

Two particularly promising interleaved pulsing schemes are evaluated in circuit simulation. It is demonstrated that an upgrade of the existing modulators utilizing the selected pulsing schemes maintains the baseline modulator-to-beam efficiency (>90%) keeping the input power quality and output pulse quality performance intact while representing a cost-effective solution for the linac upgrade to implement the proposed ESSnuSB project.

11:40am - 12:00pm
Solid State Modulators: 5

Analysis of the Triggering Instants of the Solid-State Switches of the Pulsed Power Sources for Achieving Optimal Projectile Velocity in a Multistage Induction Coilgun

R. Ram, J. T. Meledath

Indian Institute of Science, Bangalore, India

A multistage induction coilgun works on the principle of electromagnetic induction between an array of drive coils, which are wound on a long insulating barrel of appropriate length, and an electrically conducting projectile (or armature) placed inside the barrel. Previously charged high voltage capacitor banks are sequentially discharged into the drive coils through high voltage solid-state switches leading to the generation and flow of high magnitude impulse currents through the drive coils. Time-varying magnetic flux thus produced by the pulsed currents through the drive coils interact with the projectile inside and induce a resultant eddy current in it. The electromagnetic thrust (F) exerted on the projectile is a product of the excitation current through the drive coil (ic), induced current on the projectile (ip), and the mutual inductance gradient (dMcp/dx, i.e., the change in mutual inductance between the drive coil and the projectile as the projectile moves along the barrel). The higher the electromagnetic thrust is available from each stage, the higher is the launch velocity (vp) of the projectile that can be achieved after each stage. A higher dMcp/dx leads to a higher F. Now, dMcp/dx essentially depends on the radii of the drive coil and the projectile, and the distance between the midplanes of the drive coil and the projectile, i.e., the triggering instant of the pulsed power source w.r.t. the position of the projectile inside each drive coil. For a particular multistage induction coilgun design, where the radii of the drive coil and the projectile are fixed, the appropriate instant of synchronization of triggering of the stages, i.e., the optimum triggering instant of the solid-state switch of the pulsed power source w.r.t. the position of the projectile inside each drive coil, plays a vital role in achieving a higher vp of the projectile. The several stages of a multistage induction coilgun can typically be energized in two ways: (1) positive-positive (PP), where the direction of the excitation current in the subsequent drive coils is kept the same, and (2) positive-negative (PN), where the direction of the excitation current in the subsequent drive coils is reversed alternatively. The optimum triggering instant for the projectile inside each drive coil of the subsequent stages changes accordingly in these two launching configurations. This paper investigates and compares the difference in triggering instants for the projectile inside each drive coil in PP and PN launcher configurations. The analysis is carried out with a four-stage induction coilgun. The input electrical energy to each stage is kept constant. The triggering instant for the projectile inside each drive coil is then set such that the projectile position is anywhere from 0 mm to 18 mm with a linear step of 1.6 mm. The triggering position inside each drive coil is measured w.r.t. the rear end of the corresponding drive coil. The analysis presented in this paper will help better understand the operation of a multistage induction coilgun.

3:30pm - 5:30pmHigh Power Microwaves
Location: 301B
Session Chair: Jon Cameron Pouncey, Naval Surface Warfare Center Dahlgren Division
3:30pm - 4:10pm
High Power Microwaves: 1

High Power Microwave and Pulsed Power Development at the University of Michigan

N. M. Jordan, D. A. Packard, B. J. Sporer, A. P. Shah, G. V. Dowhan, S. C. Exelby, P. C. Campbell, T. J. Smith, C. J. Swenson, R. A. Revolinsky, E. N. Guerin, L. I. Welch, S. V. Langellotti, Y. Lau, R. D. McBride, R. M. Gilgenbach

University of Michigan, United States of America

The Plasma, Pulsed Power, and Microwave Laboratory (PPPML) at the University of Michigan (UM) is home to three large pulsed-power drivers: the Michigan Electron Long Beam Accelerator (MELBA), the Michigan Accelerator for Inductive Z-pinch Experiments (MAIZE), and the Bestowed LTD from Ursa Minor Experiment (BLUE). MELBA is a 7-switch Marx generator with an Abramyan circuit and is capable of generating a 10 kA electron beam at -1 MV for up to 1 µs; this accelerator is currently configured to produce -300 kV and is used for high-power microwave (HPM) research. MAIZE is a 3-m-diameter, single-cavity Linear Transformer Driver (LTD) that supplies a 1 MA, 200 ns pulse for high energy-density physics (HEDP) research. BLUE is the most recent addition to the PPPML, consisting of four 1.25 m diameter LTD cavities which were previously part of Sandia’s 21-cavity Ursa Minor facility. A single cavity of BLUE produces an estimated 150 kA at 100 kV in ~100 ns into a load matched to the driver’s 0.5 Ω impedance. The 4 cavities can be stacked for a total driver impedance of ~ 2 Ω and correspondingly increased matched-load voltage of 400 kV.

Recent HPM developments will be presented, including: a multi-frequency Harmonic Recirculating Planar Magnetron (HRPM) utilizing a dual-frequency (L-band and S-band) slow-wave structure to enable low-Q operation at the MW level; a 5 MW Recirculating Planar Crossed-Field Amplifier (RPCFA) with ~ 9 dB gain at 3 GHz; experimental demonstration of the Recirculating Planar Magnetron with Coaxial-All-Cavity Extraction (RPM-CACE); a moderate current (< 10 kA) Magnetically Insulated Line Oscillator (MILO) operating in L- and S-band; and the implementation of a GW-class MILO on the BLUE LTD.

Pulsed power developments will also be highlighted, particularly the recent improvements to spark-gap switch reliability in MAIZE. UM has tested 3 spark-gap switch designs on MAIZE, and uncovered a number of operating modes that result in inconsistent breakdown and triggering. The lessons learned from these undesirable operating conditions, and the subsequent methods to achieve reliable operation, should benefit the growing population of researchers using and designing LTDs.

Research supported by The Air Force Office of Scientific Research #FA9550-15-1-0097, FA9550-20-1-0409, and FA9550-21-1-0184, Office of Naval Research #N00014-19-1-2262, #N00014-18-1-2499, and #N00014-16-1-2353, NNSA # DE-NA0003764, DEPS Fellowship support to DP, and L3Harris Electron Devices.

4:10pm - 4:30pm
High Power Microwaves: 2

Modeling Composite Nonlinear Transmission Lines as High-power Microwave Sources

X. Zhu, A. J. Fairbanks, T. D. Crawford, A. L. Garner

Purdue University, United States of America

Nonlinear transmission lines (NLTLs) can sharpen input pulses and induce output oscillations as high-power microwave (HPM) sources with high pulse repetition rates, frequency agility, durability, and reliability, leading to compact devices with inexpensive construction costs and reduced power consumption [1]. In general, NLTLs use ferroelectric and/or ferromagnetic materials with field-dependent permittivity and/or permeability, respectively; implementing ferromagnetic materials produces microwave oscillations through gyromagnetic precession when biased under an external magnetic field [1].

In this work, we use COMSOL Multiphysics to model NLTLs containing ferroelectric and/or ferromagnetic composites and compare to experimental results. We have previously measured and simulated the linear effective electromagnetic properties of composites containing various volume loadings of barium strontium titanate (BST) and/or nickel zinc ferrite (NZF), which are nonlinear dielectric and magnetic materials, respectively [2]. We have also measured the nonlinear permeability and nonlinear permittivity of various volume loadings of these materials. These studies demonstrate the tunability of the electromagnetic properties of the composites, which may be used to adjust the RF output from a NLTL.

To reduce computational expense, we model the composite regions in the NLTLs as homogeneous domains. To model the gyromagnetic NLTLs with ferrite composites, we solve the Landau-Lifshitz equation [3] and treat the gyromagnetic ratio and damping factor as fitting parameters determined by comparison to experiments. The center frequency of the output pulses primarily varies with the gyromagnetic ratio when the bias field, the incident field, saturation magnetization of the applied ferrites, and ferrite filling ratio are fixed [3]. We compare the resulting models to experiments using NLTLs with different compositions of BST and/or NZF driven by different pulse forming lines. We then use the benchmarked model to predict performance with different materials and volume loadings to assess potential future designs. Implications for a complete HPM system design integrating an antenna and pulse forming network will be discussed.

We gratefully acknowledge funding from the Office of Naval Research (Grant No. N00014-18-1-2341).

[1] A. J. Fairbanks, A. M. Darr, and A. L. Garner, “A review of nonlinear transmission line system design,” IEEE Access, vol. 8, pp. 148606 – 148621, 2020.

[2] X. Zhu, A. J. Fairbanks, T. D. Crawford, and A. L. Garner, “Modelling effective electromagnetic properties of composites containing barium strontium titanate and/or nickel zinc ferrite inclusions from 1-4 GHz,” Compos. Sci. Technol., vol. 214, 2021, Art. No. 108978.

[3] I. V. Romanchenko, V. V. Rostov, A. V. Gunin, and V. Y. Konev, “High power microwave beam steering based on gyromagnetic nonlinear transmission lines,” J. Appl. Phys., vol. 117, 2015, Art. no 214907.

4:30pm - 4:50pm
High Power Microwaves: 3

System Design Considerations for a Nonlinear Transmission Line Used Simultaneously as a Pulse Forming Line and High-Power Microwave Source

T. D Crawford, X. Zhu, A. J Fairbanks, A. L Garner

Purdue University, United States of America

Nonlinear transmission lines (NLTLs) have been of increasing interest for pulse sharpening and high-power microwave (HPM) generation. Their compact form factor coupled with their inexpensive and rigid design makes them ideal for field implementation where system survivability is a concern.

NLTLs are just one subcomponent in the overall HPM systems structure. Recent efforts have examined using the NLTL simultaneously as both the pulse source and HPM generator by biasing the lines with a DC charging voltage [1]. While this further reduces the spatial footprint of the system, such a design has inherent complications associated with extracting the signal it generates.

This work focuses on full system design considerations when using a NLTL in the PFL format. We manufactured 10-ohm composite based NLTLs that utilize a combination of barium strontium titanate and nickel zinc ferrite encapsulated in PDMS. The output of the NLTL was coupled to a pressurized spark gap switch that closed upon reaching a sufficient charging voltage. An impedance transformer was then designed to taper the impedance to a 50-ohm standard. We demonstrate that the RF output of the NLTL is a strong function of impedance with the RF signal becoming weaker with increasing impedance. This provides additional motivation for the NLTL in the PFL format since the impedance is readily flexible since it does not need to be directly matched to a Pule Forming Network. The ability to enhance RF generation with a lower impedance may permit further reduction in device size by eliminating the need for additional systems, such as a bias magnetic field. Overall implications on system development will be discussed.

1. A. J. Fairbanks, T. D. Crawford, and A. L. Garner, “Nonlinear transmission line implemented as a combined pulsed forming line and high-power microwave source,” Rev. Sci. Instrum., vol. 92, 2021, Art. no. 104702.

4:50pm - 5:10pm
High Power Microwaves: 4

RF Output Power Detection of the RADAN MG-4 Microwave Generator

N. C. Harrison, K. Allen, J. C. Dickens, A. A. Neuber, J. Mankowski

Texas Tech University, United States of America

The RADAN series-based MG-4 Microwave Generator is a compact, high power microwave system developed by the Institute of Electrophysics in Ekaterinburg. The system features the RADAN high voltage generator which is a SINUS-series device featuring a Tesla transformer charger and a Blumlein pulse forming line. The MG-4 microwave head is a mm-band relativistic backward wave oscillator (BWO) that operates at 35 GHz with a 5 to 10 MW peak output power and a pulsewidth of 3 nsec. The typical method of output power measurement is done with a cryogenic detector supplied with the system which utilizes a germanium crystal that changes resistivity as microwave radiation is absorbed.

In order to confirm the rf output power level of the MG-4, and because the germanium crystal rf detector was unavailable, a commercially available rf envelope detector was employed. Analog Devices ADL6012 is a broadband envelope detector that operates from 2 GHz to 67 GHz at input powers up to +15 dBm. It also features a 500 MHz envelope bandwidth and 0.6 nsec output risetime capability.

The diagnostic setup features the ADL6012-EVALZ, an evaluation board with the ADL6012 offered by Analog Devices, shielded in a fitted brass box located in the far field (~60 cm) from the microwave output horn. The output mode of the MG-4 is nominally TM01 but a mode convertor allows for a TE11 output mode as well. The surrounding surfaces close to the detector are covered with attenuation foam to limit reflections that could possibly be detected and interfere with measurements. A 20 dBi receiving antenna and four high frequency attenuators are used to reduce the input power to the acceptable input range of the detector. Two equal length coax cables connect the differential outputs from the detector to two channels of a high-speed 1.5 GHz oscilloscope where the positive and negative envelopes of the pulse are captured separately. Based on the peak differential output voltage of the positive and negative signal, the input power of the detector can be determined by the typical performance characteristics curves in the ADL6012 data sheet. Lastly, accounting for the attenuators, antennas, and free space path loss, the peak output power of the MG-4 can be accurately determined. At 60 cm centered from the MG-4, the ADL6012 output a 660 mV differential voltage. Using the typical application curves in the data sheet, this corresponds to a 4.4 dBm input power into the ADL6012. Accounting for the attenuators, receiving antenna, and free space path loss, the transmitted peak power of the MG-4 is 98.17 dBm (6.56 MW). This is in the expected output power range of the MG-4.

5:10pm - 5:30pm
High Power Microwaves: 5

Compact 60kV High Voltage Capacitor Charger for UWB Electromagnetic Pulse Generator

W. C. Jeong, H. J. Ryoo

Chung-Ang University, Korea, Republic of (South Korea)

In this paper, a portable 60kV high-voltage capacitor charger for ultra-wideband electromagnetic pulse generator based on a 24V battery was described. The HVCC should charge storage capacitors up to breakdown voltage(about 55kV) of spark gap switch inside Marx generator of the ultra-wideband electromagnetic pulse generator at 100Hz repetition rate. It should be considered not only the operation specification, but also size and weight for portability, nonetheless current burden on the used components is relatively large because of low input voltage. In addition, there are other difficulties such as the voltage stress of each components and isolation from other parts like grounded case. To satisfy the requirements, a parallel loaded resonant converter which operates as high-efficiency and high-frequency and an output rectifier designed by modifying the basic Cockcroft-Walton voltage multiplier(CWVM) were applied. The parallel loaded resonant converter operating at above resonant frequency was designed with a small value of parallel resonant capacitor to reduce reactive power, crest factor of the resonant current, and conduction loss. Also, proper snubber capacitor design is applied to reduce turn off switching loss. The modified CWVM is composed of two symmetrical CWVMs charged in parallel by a center-tapped transformer and storage capacitors inside the CWVMs are connected in series to the load. With this structure, it can be alleviated the voltage stress and maximum voltage potential. Therefore, it significantly reduces the difficulty of selecting components, design of the high voltage transformer and considering insulation when manufacturing actual system. In addition, it can be operated through very simple sensorless control method, only needs the information of the time to charge the load capacitor once and repetition rate, due to the characteristics of the designed resonant converter, such as a current source characteristic and inherent maximum voltage limit. Between the HVCC and Marx generator, the conductorless high voltage cable is connected to replace the isolation resistor to block a noise generated by UWB EMP, and to limit the excessive charging speed. Finally, the HVCC was actually implemented as small(120*120*245mm) and lightweight(4kg). Various experiments with 3.2nF and 8.4nF load capacitors equivalent to the sum of storage capacitors in the Marx generator were conducted. Also, it is verified that the HVCC can charge to 62kV and be inherently limited due to the characteristic of the designed converter without any control. Finally, it was verified by the experimental result with the actual Marx generator load that the HVCC repeatedly charge over 50kV at 100Hz repetition rate.

Date: Wednesday, 22/June/2022
10:00am - 12:00pmBiomedical and Applications
Location: 301B
Session Chair: Ram Anand Vadlamani, Virginia Tech
10:00am - 10:20am
BioMed and Applications: 1

Pulsed Electric Field Activation of Platelet Rich Plasmas with Different Levels of Platelet Enrichment and Red Blood Cell Content

B. Neculaes1, A. Garner2, E. Longman2

1GE Research, Niskayuna, NY, United States of America; 2Purdue University, West Lafayette, IN, United States of America

Ex vivo platelet activation is being explored for a variety of regenerative medicine and wound healing applications. Activating the platelets releases multiple proteins and growth factors with key roles in the wound healing cascade. Platelet rich plasma (PRP) is typically obtained by centrifugation from the whole blood drawn from the patient. Bovine thrombin, a biochemical agent derived from animal sources, is then used in the clinic as the state of art platelet activator. The activated PRP, called platelet gel, is applied topically on the wound to be treated. Several studies have examined pulsed electric fields as a physically based method for platelet activation with several key advantages over bovine thrombin, including an easier workflow, the ability to standardize the method, reduced cost, enhanced tunability, and independence from animal sources that may cause immune response. Pulsed electric fields of various pulse durations [1] and delivery modality (capacitive or conductive coupling; various concentrations of extracellular calcium) [2] have been successfully used for ex vivo platelet activation in several biological matrices, including whole blood [3] and platelet rich plasma with red blood cell (RBC) content. This study presents the first results of pulsed electric field activation using three types of platelet rich plasmas from four human donors – one with RBC content and two others with minimal RBC content. Two types of microsecond pulsed electric fields have been used in this study, along with negative (no activation) and positive (activation using bovine thrombin) controls. Experimental results confirm growth factor release with pulsed electric fields for all three types of PRP – opening the door for wide clinical adoption of this novel pulsed power based biomedical approach.

[1] A. L. Garner, A. S. Torres, S. Klopman, and B. Neculaes, “Electrical stimulation of whole blood for growth factor release and potential clinical implications,” Med. Hypotheses, vol. 143, 2020, Art. no. 110105.

[2] A. L. Garner, A. L. Frelinger III, A. J. Gerrits, T. Gremmel, E. E. Forde, S. L. Carmichael, A. D. Michelson, and V. B. Neculaes, “Using extracellular calcium concentration and electric pulse conditions to tune platelet-rich plasma growth factor release and clotting,” Med. Hypotheses, vol. 125, pp. 100-105, 2019.

[3] B. Neculaes, A. L. Garner, S. Klopman, C. Morton, and A. S. Torres, “A multi-donor ex vivo platelet activation and growth factor release study using electric pulses with durations up to 100 microseconds,” IEEE Access, vol. 9, pp. 31340 – 31349, 2021.

10:20am - 10:40am
BioMed and Applications: 2

Analysis of the Role of Cellular Heating in Microsecond Irreversible Electroporation

W. J. Milestone1, Q. Hu2, A. M. Loveless3, A. L. Garner3, R. P. Joshi1

1Texas Tech University, Lubbock, TX 79409, USA; 2Eastern Michigan University, Ypsilanti, MI 48197, USA; 3Purdue University, West Lafayette, IN 47906, USA.

Irreversible electroporation (IRE) involving tumor ablation presents a minimally invasive treatment and has found a niche in oncological applications. It has proven to be a safe and effective procedure for treating many unresectable tumors. However, the use of a series of high frequency sinusoidal bipolar electric pulses, in the context of cellular drug delivery and/or irreversible electroporation, has not been studied to the best of our knowledge. This scheme, similar to the High Frequency Irreversible Electroporation (HFIRE) protocol, could prove to be of utility and synergistic effects of local membrane heating might well be beneficial in the context of this long wavetrain. In the present simulation study, two aspects of interest will be probed: (i) the role of cell heating in possibly promoting the successful uptake of drugs for treatment, and (ii) the possible synergistic interplay between the electric field and local membrane heating in reducing the required electroporation threshold.

In this work, membrane electroporation will be simulated based on a Smoluchowski continuum analysis discussed elsewhere by our group, together with spatio-temporal heating due to the power dissipation from the external bi-phasic source. We will consider two-dimensional transient heat flow with azimuthal symmetry in a single spherical cell. The following aspects will be analyzed and discussed in this presentation: (i) Changes induced by including heating, especially effects on pore formation dynamics. (ii) Quantitative assessment of the magnitude of heating caused by the applied electric fields and its dependence on wavetrain and field characteristics. This could define safe-operating limits and/or provide guidance towards optimum parameter space. Given that the vast parameter space depends on multiple factors, including cell size, pulse characteristics, electrical and thermal parameters of the biological system, applied waveforms, and number of pulses, only a few test cases will be probed. (iii) The present simulations will allow predictions and mechanistic insights into the level of electric field threshold reductions possible due to synergistic heating. (iv) And finally, the possibility of establishing large thermal gradients at the membrane for thermo-diffusive transport will also be quantitatively assessed.

10:40am - 11:20am
BioMed and Applications: 3

Enhanced inactivation of Gram-negative bacteria using Gram-positive antibiotics and nanosecond electric pulses

R. A. Vadlamani1, A. Dhanabal2, D. A Detwiler3, R. Pal1,2, J. McCarthy3, M. N Seleem1,2, A. L Garner2

1Virginia Tech; 2Purdue University; 3Nanovis

Physically disrupting microorganism membranes with electric pulses renders the resistance mechanisms that inhibit or excrete antibiotics inert, reducing the antibiotic dosages required and making ineffective antibiotics effective. The growing threat of antibiotic resistant infections combined with a lack of drugs in the discovery pipeline necessitates novel ways for enhancing existing antibiotic effectiveness [1]. Nanosecond electric pulses (NSEPs) can make Gram-positive antibiotics, which are abundant, effective against Gram-negative resistant strains of bacteria, for which new and effective medicines are sorely lacking, on a sufficiently short timeframe to prevent resistance mechanisms from developing. We demonstrate the synergistic inactivation of a Gram-positive (Staphylococcus aureus) and two Gram-negative (Escherichia coli, and Pseudomonas aeruginosa) bacteria by combining various antibiotics with different mechanisms of action with 222 30 kV/cm or 500 20 kV/cm, 300 ns duration electric pulses (EPs) [2], energy matched [3] but selected such that the lower electric fields had minimal impact on viability, but reacted synergistically in combination with antibiotics. Combining NSEPs with antibiotics induced several log-reduction of colony forming units for antibiotics that induced no inactivation following 10 minutes of exposure in solution without NSEPs. Staphylococcus aureus inactivation improved compared to EPs alone when we combined 2 mg/L or 20 mg/mL of rifampicin with the 30 kV/cm EPs; however, only a few of the other combinations enhanced inactivation. E. coli inactivation improved compared to EPs alone by combining either EP pulse train with 2 mg/L or 20 mg/mL of mupirocin or rifampicin or by combining the 30 kV/cm EPs with either 2 mg/L or 20 mg/mL of erythromycin or vancomycin. These results indicate that EPs can make Gram-positive antibiotics efficient for inactivating Gram-negative bacteria.

[1] D. S. Davies and E. S. Verde, “Antimicrobial resistance,” Search Collab. Solut. World Innov. Summit Health Doha, pp. 1–36, 2013.

[2] A. Vadlamani, D. A. Detwiler, A. Dhanabal, and A. L. Garner, “Synergistic bacterial inactivation by combining antibiotics with nanosecond electric pulses,” Appl. Microbiol. Biotechnol., vol. 102, no. 17, pp. 7589–7596, 2018.

[3] K. Schoenbach, R. Joshi, S. Beebe, and C. Baum, “A scaling law for membrane permeabilization with nanopulses,” IEEE Trans. Dielectr. Electr. Insul., vol. 16, no. 5, pp. 1224–1235, Oct. 2009.

11:20am - 11:40am
BioMed and Applications: 4

Using intense pulsed electric fields for the sterilization of solid pre-packed food – the design and preliminary testing of a practical MV-class system

M. Woodyard, B. Novac, P. Senior, J. Stobbs

Loughborough University, United Kingdom

A pulsed power MV-class system for generating intense pulsed electric fields in a very large volume of water was designed, manufactured and tested. This is a first and essential step towards the proof-of-principle demonstration of a novel technique for the non-invasive sterilisation of pre-packed food. The pulsed power system, based on MV Tesla transformer technology, is capable of producing pulsed electric fields in excess of 100 kV/cm in a massive volume (≈1 L) of water. The electric field distribution in the processing volume is obtained using a commercially available electrostatic solver, benchmarked using an electro-optic Kerr-effect assembly. The paper presents a detailed analysis of the unique processing unit and theoretically explores a possible scenario related to processing pre-packed food.

11:40am - 12:00pm
BioMed and Applications: 5

Resonant Charging Circuit for a Semiconductor-based Marx Generator for an Electropoation Device

M. Sack, D. Herzog, J. Ruf, G. Mueller

Karlsruhe Institute of Technology, Germany

Electroporation devices for the treatment of plant material in a continuous flow may employ a Marx circuit featuring parallel charging and a complete discharge of the capacitors during each pulse. Thereby, the use of semiconductor switches rather than spark gap switches allows for a modern design without the need of recurring maintenance of the spark gap switches. However, the use of semiconductor switches demands for an adaptation of the circuit to the properties of these switches being able to operate at lower voltage and current but higher pulse repetition rate compared to spark gap switches. For such a design, resonant charging turned out to be of advantage because it combines a fast energy transfer from a DC-link capacitor as part of the power supply to the stage capacitors of a Marx generator with a charging circuit having no active switches. Moreover, it enables an increase in the charging voltage by a factor of approximately two with respect to the DC-link voltage.
An 8-stage Marx circuit with a stage voltage of 1 kV has been set up to study resonant charging. Its charging path has been equipped with current-compensated chokes having a low inductance during charging and a high inductance for transient insulation of the stages during the pulse generation. The charging circuit has been designed for a peak current of 70 A and a charging time of 800 µs. A separate inductance between the DC-link capacitor of the power supply and the generator serves as the inductive component for the resonance circuit. As pulse switches IGBTs have been employed. In the course of the charging process, they serve as opening switches allowing for fine tuning of the charging voltage in repetitive operation. The generator has been operated either with a ground connection at its negative output terminal or grounded at its center to deliver a ground-symmetric output voltage. In both cases the magnetic energy stored inside the current-compensated chokes has been either degraded or recycled to prevent the cores from saturation. In the latter case, measurements revealed oscillations in a resonant circuit comprising the stray capacitance of the current-compensated chokes. A series diode avoids these oscillations. The paper describes selected details of the circuit design and presents measurements of the charging process.

3:30pm - 5:30pmAnalytical Methods
Location: 301B
Session Chair: Amanda M. Loveless, Purdue University
3:30pm - 3:50pm
Analytical Methods: 1

Comparison of Particle-in-Cell and Continuum Simulations for RF Microscale Gas Breakdown

A. M. Loveless1, V. Ayyaswamy2, S. Mahajan1, A. Semnani3, A. L. Garner1

1Purdue University, United States of America; 2University of California Merced, United States of America; 3University of Toledo, United States of America

Understanding and accurately characterizing electron emission and gas breakdown is necessary with increasing device miniaturization. For DC voltages, Paschen’s law, which is based on the Townsend avalanche criterion, is commonly used to predict gas breakdown; however, for microscale gaps, the resulting strong electric fields at breakdown induce the release of additional electrons by field emission (FE), which considers the enhanced surface electric field due to the decreased potential barrier at the cathode [1]. Accurately predicting breakdown under these conditions requires combining field emission and Townsend avalanche. Similarly, field emission also contributes to breakdown for microscale gaps under RF and microwave fields, motivating theoretical studies and particle-in-cell (PIC) simulations [2] to account for this behavior. While effective for gaps below ~10 microns at atmospheric pressure, PIC is not computationally efficient for larger gaps due to the computational expense encountered with additional particles. Thus, this study compares RF breakdown simulations using PDP1, a 1D/3v (one-dimensional in space, three-dimensional in velocity) PIC code, to continuum simulations using SOMAFOAM [3], a finite volume framework to simulate low-temperature plasmas. The results between PDP1 and SOMAFOAM will be compared to each other and theory for various frequencies, pressures, and gap distances, particularly to assess scaling laws between these parameters in different operational regimes. The computational efficiency of the two methods and assessment to theory and experiment will be discussed.

[1] A. L. Garner, A. M. Loveless, J. N. Dahal, and A. Venkattraman, “A tutorial on theoretical and computational techniques for gas breakdown in microscale gaps,” IEEE Trans. Plasma Sci., vol. 48, pp. 808-824, 2020.

[2] M. U. Lee, J. Lee, J. K. Lee, and G. S. Yun, “Extended scaling and Paschen law for micro-sized radiofrequency plasma breakdown," Plasma Sources Sci. Technol., vol. 26, art. no. 034003, 2017.

[3] A. K. Verma and A. Venkattraman, “SOMAFOAM: An OpenFOAM based solver for continuum simulations of low-temperature plasmas,” Comp. Phys. Comm., vol. 263, art. no. 107855, 2021.

Work supported by the Office of Naval Research under Grant Number N00014-21-1-2441.

3:50pm - 4:30pm
Analytical Methods: 2

Crossed-Field Nexus Theory: Incorporating Collisions, Field Emission, Thermionic Emission, and Space-Charge

L. I. Breen1, A. M. Loveless1, A. M. Darr1, K. L. Cartwright2, A. L. Garner1

1Purdue University, West Lafayette, IN 47906 USA; 2Sandia National Laboratories, Albuquerque, NM

Understanding electron emission is vital for characterizing diode performance for numerous applications, including directed energy systems, thermionic converters, time-resolved electron microscopy, and x-ray systems. The “nexus theory” formulation may be used to predict the physical conditions where multiple electron emission mechanisms, such as thermionic, field, and space-charge limited emission, may need to be solved jointly [1]. Once nexus theory identifies such a regime, one can derive exact equations from first principles that couple the relevant physics to assess behavior. The exact model should recover the standard equations for the individual emission mechanisms under appropriate asymptotic limits [1]. Operating conditions near where these asymptotic solutions match require more complicated equations coupling the relevant mechanisms; regimes farther away from these intersections may use the simpler, well-known solutions.

A common diode design in high power applications incorporates an external magnetic field perpendicular to the electric field induced by the applied voltage. Electron trajectories in these crossed-field diodes may either cross the gap if the magnetic field is below a limiting value known as the Hull cutoff or be turned back to the cathode for magnetic fields exceeding the Hull cutoff. Above the Hull cutoff, the diode is magnetically insulated. Much as the Child-Langmuir equation characterizes planar space-charge limited current (SCLC), similar equations may be derived for the limiting current in crossed-field diodes under non-magnetically insulated [2] and magnetically insulated conditions [3]. These conditions do not strongly depend on the specific electron emission mechanism, but rather define the maximum current that may be emitted into the gap based on geometry and boundary conditions.

This presentation highlights our application of nexus theory to crossed-field diodes. We unify thermionic and field emission with the limiting current in a crossed-field diode by introducing the generalized thermal-field emission current density equation, as was previously derived for non-magnetic diodes [1]. We will next introduce collisions into the derivation of the limiting current of crossed-field diodes [2,3] to derive a collision limiting current for a crossed-field diode, equivalent to a Mott-Gurney law for non-magnetic SCLC with collisions. The implications of the transitions between these mechanisms under various conditions and the respective limits on device operation will be discussed.

1. A. M. Darr, C. R. Darr, and A. L. Garner, “Theoretical assessment of transitions across thermionic, field, and space-charge-limited emission,” Phys. Rev. Res., vol. 2, 2020, Art. no. 033137.

2. Y. Y. Lau, P. J. Christenson, and D. Chernin, “Limiting current in a crossed-field gap,” Phys. Plasmas, vol. 5, pp. 4486-4489, 1993.

3. P. J. Christenson and Y. Y. Lau, “Transition to turbulence in a crossed‐field gap,” Phys. Plasmas, vol. 12, pp. 3725-3727, 1994.

4:30pm - 4:50pm
Analytical Methods: 3

Novel techniques for deriving the space-charge limited current for nonplanar diodes

N. R. Sree Harsha, A. M. Darr, J. M. Halpern, A. L. Garner

Purdue University, United States of America

Space-charge-limited current (SCLC) is the maximum current that can flow in the steady-state operation of the diode. Characterizing SCLC is critical for understanding the behavior of various devices, including high-power vacuum devices, organic field-effect transistors, quantum diodes, n-i-n or p-i-p diodes, and photovoltaic devices [1]. The SCLC in a one-dimensional (1-D) planar diode was derived independently by Child and Langmuir over a century ago [1]. Recently, we applied variational calculus (VC) and conformal mapping (CM) to derive analytic solutions to SCLC for nonplanar diode geometries [2].

In this presentation, we review the application of VC and CM to obtain analytic solutions for SCLC for nonplanar diodes. The analytic solutions for SCLC in any orthogonal coordinate system can be obtained using VC by extremizing the total current in the gap [2]. While VC is a powerful technique to solve for SCLC, the calculations become tedious for diodes exhibiting curvilinear flow. For such geometries, we have applied CM to transform the curvilinear flow into a rectilinear flow, thereby obtaining analytic SCLC solutions [2]. We extend VC to obtain a mathematical relationship between vacuum potential and space-charge-limited potential in any orthogonal geometry [3]. The exact solutions for SCLC in two-dimensional and three-dimensional planar diodes with finite emitters are presented [3]. We also apply Lie point symmetries to derive SCLC with nonzero injection velocity in nonplanar diode geometries and describe how similar solutions may be obtained using VC. The practical importance of this flexibility and a comparison between these mathematically powerful techniques will be discussed.

[1] P. Zhang, Y. S. Ang, A. L. Garner, Á. Valfells, J. W. Luginsland, and L. K. Ang, “Space–charge limited current in nanodiodes: Ballistic, collisional, and dynamical effects,” J. Appl. Phys., vol. 129, no. 10, Mar. 2021, Art. no. 100902.

[2] A. L. Garner, A. M. Darr, and N. R. Sree Harsha, “Calculating space-charge limited current density for general geometries and multiple dimensions,” IEEE Trans. Plasma Sci., submitted.

[3] N. R. S. Harsha, M. Pearlman, J. Browning, and A. L. Garner, “A multi-dimensional Child–Langmuir law for any diode geometry,” Phys. Plasmas, vol. 28, no.12, Dec. 2021, Art. no. 122103.


This material is based upon work supported by the Air Force Office of Scientific Research under award number FA9550-19-1-0101 and a Purdue Doctoral Fellowship.

4:50pm - 5:10pm
Analytical Methods: 4

Assessment of Techniques for Determining Space-Charge Limited Current for Non-planar Crossed-field Diodes

H. Wang, N. R. Sree Harsha, A. M. Darr, A. L. Garner

Purdue University

The maximum stable current that can flow in a diode, known as the space-charge limited current (SCLC), is essential for numerous applications, including nano vacuum transistors, electric thrusters, and time-resolved electron microscopy. Recently, several general approaches for deriving analytic solutions for non-planar and multidimensional diodes have been developed [1]. Crossed-field diodes (CFDs), where an external magnetic field B is applied perpendicular to the electric field, may also be characterized by a maximum current that depends on whether an emitted electron crosses the gap or turns back to the cathode [2]. Unlike non-magnetic SCLC, the space-charge limit does not characterize the maximum current in a CFD, which is instead determined by electron flow stability [2]. These initial studies derived solutions for the limiting current that were only valid for planar diodes [2], which are not representative of typical crossed-field devices.

This presentation assesses various approaches to derive the limiting current for non-planar diodes. We first describe the derivation of the SCLC in both magnetically insulated and non-insulated CFDs by using the Euler-Lagrange equation for planar and concentric cylinder diodes [3]. While this approach may, in principle, be extended to any general geometry, the actual mathematical application is daunting. Thus, we also apply conformal mapping, which was used to derive the mapping of the space-charge limited potential from a given geometry to the standard planar geometry, to obtain SCLC for concentric cylinders [1]. We next apply Lie point symmetries, which may be considered as a generalization of conformal mapping, to derive SCLC in other complicated geometries, including concentric spheres, which are not amenable to conformal mapping [1]. An overall assessment and comparison of the SCLC using these different techniques will be discussed, as will the extension of conformal mapping and Lie point symmetries to more complicated geometries.

[1] A. L. Garner, A. M. Darr, and N. R. Sree Harsha, “Calculating space-charge limited current density for general geometries and multiple dimensions,” IEEE Trans. Plasma Sci., submitted.
[2] P. J. Christenson, “Equilibrium, stability, and turbulence in cycloidal electron flows in crossed electric and magnetic fields,” Ph.D. dissertation, Department of Nuclear Engineering and Radiological Sciences, University of Michigan, 1996.
[3] A. M. Darr, R. Bhattacharya, J. Browning, and A. L. Garner, “Space-charge limited current in planar and cylindrical crossed-field diodes using variational calculus,” Phys. Plasmas, vol. 28, no. 8, 2021, Art. No. 082110.

5:10pm - 5:30pm
Analytical Methods: 5

Optimization of a Set of Electron-Neutral Collision Cross Sections in Fluorinated Nitrile (C4F7N)

M. Flynn, A. Neuber, J. Stephens

Texas Tech University, United States of America

Plasma fluid models for high-voltage gaseous discharges rely on transport coefficients which are often calculated with an electron swarm kinetic model (e.g. Monte Carlo, Boltzmann equation). These calculations, however, require the input of a set of electron-neutral cross sections which are not well known for many gases. C4F7N (i.e. 3M™ Novec™ 4710) is one such gas. Owing to its short atmospheric lifespan and large dielectric strength, C4F7N has received recent attention as an insulating gas with significantly reduced global warming potential, when compared to SF6.

This report details the progress made in the development of a complete and self-consistent set of cross sections for electron swarms in C4F7N. MultiBolt, a multi-term Boltzmann equation solver, is utilized to optimize elastic and inelastic cross sections for the calculation of swarm parameters, which are compared with available literature. The cross section optimization procedure and considerations for the Boltzmann model will be discussed.

SNL is managed and operated by NTESS under DOE NNSA contract DE-NA0003525


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