Poster 2: 1
Design and Implementation of the SML Modulators for the ESS Linac
1Lund University, Sweden; 2European Spallation Source ERIC
The European Spallation Source (Lund, Sweden) is an under construction multi-disciplinary research facility to be based around a Linear Particle Accelerator which is to provide 2.86 ms long proton pulses at 2 GeV at a pulse repetition rate of 14 Hz, representing an average beam power of 5 MW. To accommodate the requirements of the proton linac, a large number of klystrons driven by solid state modulators rated for pulse amplitude 115 kV/100 A, pulse length 3.5 ms, pulse repetition rate 14 Hz, and pulse rise time on the order of 120 µs are required. These klystron modulators implement the novel Stacked Multi-Level (SML) modulator topology.
In the SML topology, the input stage capacitor chargers are based on an AC/DC Active Front End (AFE) rectifier and DC/DC buck converter chain. The AFE generates a stable dc-link voltage while shaping the line current to be sinusoidal and in phase with the line voltage, effectively eliminating line current harmonics and reducing reactive power to a minimum. The DC/DC converter connects the dc-link to the main capacitor bank energy storage via an inductive link, controlling the charging current to exhibit inverse waveform with respect to the capacitor bank voltage such that the required energy is replenished just in time for the following pulse, yielding constant power charging and thus flicker mitigation despite the high power pulsed load. Pulse generation is achieved in a pulse modulation/demodulation scheme as follows. First, a DC/AC inverter (H-bridge) generates an AC square voltage waveform fed to a high voltage high frequency (HVHF) transformer providing voltage amplification. Then, the amplified voltage waveform is rectified in an AC/DC high voltage diode rectifier stage and subsequently filtered, re-creating the fundamental shape of the output pulse. The topology is modular, with the implemented modulators for the ESS Linac utilizing three parallel connected input capacitor chargers and six series connected high voltage modules, increasing system power density and facilitating maintenance.
This paper presents key points, the working principle as well as the design and control of these modulators while highlighting the details of their practical implementation. Issues related to optimization, high voltage design (e.g. field control and details on the use of 3D finite element electromagnetic analysis in design), modeling and mitigation of circulating currents due to parasitic capacitive elements, and thermal management/lifetime considerations of IGBTs in high power pulsed applications are treated. Experimental results and efficiency measurements obtained in full power testing of the implemented modulators are presented.
Poster 2: 2
Triggered Spark Gap Evaluation and Optimization for Low Jitter, High Reliability Applications
Lawrence Livermore National Laboratory, United States of America
This paper discusses the evaluation and performance of three-electrode triggered spark gap switches for use in a low turn-on jitter, low pre-fire probability tolerant application. Turn-on jitter, turn-on delay time, pre-fire/no-fire occurrence, and shot life were recorded using an automated testbed for High Energy Devices TA5.0 and Excelitas GP489 spark gaps. The spark gaps were tested at 3.5kV with 1.2kA of peak current and 10mC of charge transferred per shot. The testbed apparatus and data results are shown for trigger modes A, B, and C using manufacturer-recommended triggering circuitry. Spark gap failure modes and optimum trigger modes are identified. A method for minimizing turn-on jitter using a nanosecond rise time trigger circuit with optimized trigger pulse energy for the TA5.0 spark gap is shown which achieves turn-on jitter less than 2ns.
This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.
Poster 2: 3
Pulsed Power Supply for Magnet Quench Training
Fermi National Accelerator Laboratory
Superconducting magnets typically go through a series of spontaneous “training” quenches as their current is increased towards its design value. A device has been designed and built to boost the magnet current at the moment a quench has been detected to possibly decrease the number of these quenches. The aim of the boost is to drive the magnet coil further along towards its maximum current with each training quench, and hence reduce the number of quenches required.
The current boost is accomplished by diverting the current in the magnet circuit from a diode in series with the load to a charged capacitor ( 400 mF charged to 1 kV) connected across the diode. The output terminal of the capacitor is connected to the cathode of the diode by closing IGBT switches. The connection initially adds 1 kV to the magnet voltage and drives its current up rapidly. The voltage on the capacitor bank discharges to zero as its stored energy transfers into an increase in magnet current above the quench level. The energy transfer time is some tens of milliseconds, after which the magnet protection is initiated.
The circuit has been built and is being commissioned. The design, protection systems and tradeoffs will be discussed.
Poster 2: 4
A 300 kA Pulsed Power Supply for LBNF
1Fermi National Accelerator Laboratory; 2SLAC National Laboratory
The Long Baseline Neutrino Facility (LBNF) will produce the world’s most intense neutrino beam. Three series connected magnetic horns will require 5 kV, 300 kA, 800 µs pulses at a rate of 0.7Hz to focus the beam. Fermilab has designed and built pulsed high current supplies for horns in the past. Pulsed currents of 205 kA for Neutrinos at Main Injector (NuMI / NOvA), focusing a 120 GeV beam, and 170 kA for Booster Neutrino Bean (BNB / MiniBooNE) for focusing an 8 GeV beam have been operational for about 18 years. It is required that the LBNF horn power supply last the lifetime of the project, 30 years.
A resonant, half sine wave pulser was used for NuMI and BNB and has many practical advantages. The system has impedance limited fault currents by design, albeit large ones. The pulse length of 800 µs is needed to meet the required flatness of the focussing field. The resonant behavior means that thyristor switches are well suited for this application. The design will continue the use of many pulser circuits in parallel to provide the high current. Only 30% of the initial energy stored in the capacitors is lost, based on load estimates, so an energy recovery system that is also resonant will be used to reduce charging supply size. Many fault modes of the system have also been calculated. Several circuit changes were incorporated so that a single fault can be tolerated. The supply must also be reversable to enable both neutrinos and anti-neutrinos to be produced. The reversal requirement required a significant amount of mechanical design features as the first horn must always be at the lowest potential. This requires the output polarity to change and reversal of all the semiconductors. Further design considerations will be discussed, and prototyping has begun.
Poster 2: 5
High-Speed Imaging of Exploding Detonators
1Los Alamos National Laboratory, United States of America; 2Texas Tech University; 3Scientific Applications & Research Associates
Approved for public release; distribution is unlimited.
An experiment for imaging detonators used in explosively driven pulsed power applications with high-speed, short exposure time cameras will be described in the work to follow. Three, commercially available, high intensity, pulsed xenon light sources (> 107 candela intensity) yielded unsatisfactory image quality with a minimum exposure rate (~320 k frames per second). Above 320 k frames per second, the combined output intensity of the light sources were too dim. Due to this, a lamp system was designed that would be capable of delivering higher light intensity to the target.
Two types of lamp arrays were designed and tested. The first was a large lamp array comprised of a couple high energy flash lamps, while the second was a small lamp array comprised of many low-energy flash lamps. The large lamp array was intended for multiple shot use, and was placed behind a protective sheet of polycarbonate to separate the bulbs from the detonator. The second small lamp array with low-cost flash lamps was intended for one time use and will be placed closer to the detonator. Multiple five stage, Rayleigh Pulse Forming Networks (PFNs) were developed to find the optimal energy for the flash lamp array. Each PFN was modeled using LTSpice circuit simulator to verify proper operation, and help with optimization. Experimental measurements were taken of the PFN’s voltage and current outputs and compared to simulated values. A photodiode was used to measure relative light intensity from the different lamp arrays.
Poster 2: 6
The next step progress for a skin effect opening switch construction ( the resistive version)
free, Russian Federation
The next step progress for a skin effect opening switch construction
( the resistive version)
Moscow, Troitsk, Russian Federation, 108841.
A skin effect opening switch based on a transformer inductive energy storage (LSEOS) was offered for consideration in [1-2] and its resistive version (RSEOS) was offered in  too. The latter possesses some properties of contactors. For example, it is able to carry kiloamperes current during one second and more with minimal losses. Combined with auxiliary elements (an opening switch, a capacity bank and others) the version RSEOS is converted to an opening switch configuration, where the version RSEOS gets dynamic properties. Embedded in pulsed power generator based on inductive storage as a component, the received configuration of RSEOS requires the generator adaptation to a load. There are many different loads: -inductive, resistive, nonlinear and others kind of one. Each of them claims itself approach to solve a problem of adaptation. Realized by a developing technology, an engineered impulse device is able to generate nanosecond high-voltage pulses. It lets to solve some pulsed power tasks effectively, for example, a pulse train generation of a terawatt level using direct current. Besides energy storage and its output to a load is concurrent activities .
There are many parameters of pulsed power generator exerting influence on a pulse form in a load. Some of them are the parameters of a high-ohm layer RSEOS, such as depth, d, and conductivity, ρ. A time current diffusion in a solid-state conductor is tdif = (d2μ0/4ρ), where μ0=4π∙10-7 H/m. It is obviously that changing conductivity ρ, the time characteristics of the pulse changes, especially its the trailing edge too. Influence of heating and melting of the high-ohm layer on a pulse form during pulse generation for different amount of current density is discussed in this presentation. All computations were performed for a resistive load. The offered construction of RSEOS is reusable. It lets to expand a field of application.
1. O.G. Egorov, “Pulsed power generator based on inductive storage and skin-effect opening switch (energy correlation and technical application)“ Proc. PPC, Brighton, UK, June, 2017, p.280
2. O.G. Egorov, Patent No.2680343 “The method of energy output form transformer inductive storage to a load.” Patent of Russian Federation, 02.11.2017.
3. O.G. Egorov “Combination of skin-effect opening switch and auxiliary opening switches for inductive storages application (narrowband and wideband devices)” Proc. PPC, Denver, USA, December, 2021. (to be published).
Poster 2: 7
SLAC LINAC Sub-booster Modulator Upgrade with Solid State Switch
SLAC National Accelerator Lab, United States of America
The LINAC sub-booster modulator was designed in the 1960s and has serviced SLAC LINAC about 60 years without primary switching upgrade. The primary switch for the high power pulse are two parallel vacuum tetrodes. Recently the vacuum switch price has surged, probably because more and more customers have shifted to the solid-state switch from the vacuum switch. Anticipating the vacuum switch will finally become obsolete, some solid-state switches have been tested and their performance evaluated in SLAC LINAC sub-booster modulators. In this paper, the design and performance will be reported.
Poster 2: 8
X-Band TWT Transmitter
Diversified Technologies, Inc., United States of America
In 2021 Diversified Technologies, Inc. (DTI) developed and installed a high power X-band transmitter into a new radar. The transmitter’s design is closely based on several high power traveling-wave tube (TWT) transmitters previously delivered by DTI. This X-band transmitter employs the Communications and Power Industries’ (CPI) TWT, model VTX-5681B3, to deliver a peak power of 130 kW at 35% duty. DTI built the modulator and other electronics subsystems, purchasing and integrating the RF systems for the transmitter, as well as providing cooling on a dish antenna. This on-mount arrangement gives the most direct waveguide run from the TWT to the antenna feed network, resulting in the lowest microwave losses and maximum transmitted power. The remainder of the transmitter electronics are mounted on the ground near the antenna pedestal in a DTI-supplied shelter. A single DTI-supplied cooling skid provides system cooling for both transmitters delivered.
DTI’s X-band transmitter consists of state-of-the-art, solid state, high-voltage subsystems. The speed, precision, and reliability of solid state devices offer a level of performance unattainable in conventional transmitter designs. The only vacuum electron device (VED) in the transmitter is the CPI VTX-5681 very high power coupled-cavity TWT.
Poster 2: 9
High Stability Klystron Modulator for Commercial Accelerator Application
Diversified Technologies, Inc., United States of America
Diversified Technologies, Inc. (DTI) designed and developed a high stability modulator system for a commercial linear accelerator application. The DTI modulator delivers significant advantages in klystron performance through highly reliable functionality as well as flicker- and droop-free operation from 50-500 μs up to 400 Hz (duty limited). The main assemblies on the DTI system consist of a controls rack, high voltage power supply (HVPS), modulator, and cooling manifolds for the modulator, high voltage power supply and klystron tube. Two HVPS (upgradeable to four) provide stable and accurate DC voltage which is used to drive a CPI VKP-8352C UHF-band pulsed klystron for the linear accelerator. A solid state series switch, based on DTI’s patented design, provides both pulse control and arc protection to the klystron. Operating with four HVPS, the DTI modulator is able to operate at a maximum average power of ~750 kW at 105 kV, 47 A nominal. At the end of the initial contract, DTI provided two systems and a total of four HVPS (two of which are used with each system).
Poster 2: 10
Aluminum electrolytic capacitor vulnerability evaluation in DC power supplies at the Spallation Neutron Source
Oak Ridge National Laboratory, United States of America
The service life of electrolytic capacitors is a concern for long-term reliable operation of power supplies. The Power Conversion Group at the Spallation Neutron Source (SNS) facility of Oak Ridge National Laboratory is responsible for more than 500 power supplies with over 1000 electrolytic capacitors installed in these power supplies. Most of the electrolytic capacitors are in operation since 2007 and are either well over or close to the manufacturer provided lifetime. This paper addresses this vulnerability to ensure continued reliable operation of the SNS. The power supply circuit will be simulated in a MATLAB/Simulink environment to quantify the capacitor ripple current and operating voltage. Combined with manufacturer data, this information will be used to estimate capacitor lifetime. Utilizing the simulation results and lifetime projections of the capacitors, capacitor replacements for the power supplies will be prioritized. To assess end-of-life, the ambient temperature and ripple current of the capacitor is used. Based on the manufacturer’s data and scientific literature review, capacitor end-of-life will be established. The results of the simulations and analysis will be presented. Data on the highest priority supplies will also be presented, and statistics on the capacitor performance, reliability and remaining lifetime will be shown.
Poster 2: 11
Duty Cycle Adjustable High-Voltage AC Power Supply with High Repetition Rate
1INSTITUTE OF ELECTRICAL ENGINEERING,CHINESE ACADEMY OF SCIENCES, China, People's Republic of; 2University of Chinese Academy of Sciences
Low-temperature plasma has a wide range of applications and unique superiority in environmental pollution improvement, biomedicine, materials modification and energy conversion due to its electrical and physical properties. For industrial applications, adopting AC power supply for generating plasma is also a most common method due to high stability of system. However, the application of ac mode also brings forward the demand of more efficient operation modes which include alterable duty cycle , adjustable amplitude of output voltage and repetition rate. To decreasing the dimension of whole systems, we sacrificed some adjustable range of variable parameters. The main circuit of presented power supply utilize push-pull circuit since no need for considering potential problems of gate drive for switches, and the auxiliary circuit consists of dual channel output gate driving circuit with adjustable duty cycle and step-down circuit. As a result, the AC power supply can generate output voltage~6 kV, peak repetition rate ~20kHz, which is expected to be applied in DBD load in the future for demonstration of generating plasma.
Poster 2: 12
A high-power pulse resistor with nonlinear low inductance
1Hefei University of Technology, China, People's Republic of; 2Hefei Hangtai Electrophysics Co. Ltd
High-power pulse resistor used in surge current Marx generator shall adjust the current waveform with desired inductance. However, the demand of low inductance is always conflicted to the size of resistor for its low resistance with surge current lager than 10kA. To break through the limited application, here, a high-power pulse resistor of multi-conductor coaxial structure, made out of ferromagnetic material (OCr25Al5), that works in magnetic saturation is designed. Our test results showed that the resistor is about 400mΩ, the inductance decreases nonlinearly with current amplitude and could be much small as 1.7μH in 30kA. This inductance allows the resistor meets lots of surge current generator requirements, especially in lightning current waveform generation. More importantly, the resistor size compared to general pulse resistors decreased vastly. Our study illustrates that that resistor design could be well used in supporting generation of high-amplitude pulse current waveform.
Poster 2: 13
A low cost, fast rise time, 120 kV multiple use Pulsed Power trigger generator
Loughborough University, United Kingdom
A pulsed power trigger generator is introduced, having a simple design based on ceramic capacitor stacks having a total capacitance of 5.3 nF, mounted inside an oil-filled cylindrical-coaxial transmission line. After being charged to 120 kV, the unit is discharged by a self-breakdown spark-gap switch, generating an output voltage impulse with a rise time of only a few ns. Experimental data is provided for the pulsed generator operated with various loads.
Poster 2: 14
An Experimental Apparatus for Novec 4710 for Pulsed Power Applications
1Texas Tech University, United States of America; 2Lawrence Livermore National Laboratory
Sulphur hexafluoride (SF6) is a prevalent insulating gas in high voltage environments. However, the high global warming potential of SF6 has motivated a search for an alternative, more environmentally friendly insulating gas. Novec 4710 (C4F7N) is a primary candidate due to potentially having nearly twice the voltage hold-off of SF6, significantly lower atmospheric lifetime, and a greatly reduced greenhouse effect.
While prior work has focused chiefly on DC and AC (power utility) frequencies, an experimental apparatus was developed to assess the pulsed power performance characteristics of Novec 4710 in mixtures with CO2 and N2 at pressures of up to three atmospheres. The pressure chamber has interchangeable anode and cathode connections to facilitate the testing of multiple breakdown geometries such as plane-to-plane, rod-to-plane, et cetera. The electrode design permits the study of various electric field gradients on the hold-off voltage of Novec 4710. Within the chamber, the electrodes are integrated as center conductors in a 50 Ohm coaxial transmission line geometry. Thus, the system maintains 50 Ohm impedance throughout the geometry, thereby minimizing reflections and allowing for voltage and current diagnostics with fast, nanosecond resolution.
Poster 2: 15
Development of a Magnetron based S-band High Power Microwave Test Bed
Texas Tech University Center for Pulsed Power and Power Electronics
This poster reviews a magnetron based high power microwave (HPM) system and subcomponents for producing ~2.5 MW HPM pulses with ~ 3.6 µs pulse duration. This system utilizes a 5-stage, 25 Ohm, Guillemin quasi-type-E pulse forming network (PFN), initially charged to 24 kV. The PFN delivers 12 kV to a matched load, which consists of a 1:4 transformer to drive a high power magnetron (EEV M5193) with up to 48 kV and 110 A (~400 Ohm effective impedance). The electrical performance characteristics of the PFN with resistive load terminations are reported and compared with circuit simulation. Preliminary HPM performance characteristics are reported.
Poster 2: 16
Design Challenges in High Current Pulsed Striplines
Fermilab, United States of America
The Long Baseline Neutrino Facility (LBNF) will produce the world’s most intense neutrino beam. Three series connected magnetic horns will require 5kV, 300kA, 800µs pulses at a rate of 0.7Hz to focus the beam. Connecting a single power supply to these focusing horns will require a low impedance connection measuring over 60 meters in length. In order to meet the challenging requirements of connecting the horns to the power supply, this connection is engineered as a nine-conductor, high-current pulsed stripline. It must pass through a harsh radiation environment, be passively cooled, and have an operational lifetime of at least 30 years. This paper discusses mechanical and electrical considerations such as high-voltage holdoff, clamped joint performance, and Lorentz force mitigations in order to meet the specified requirements. The results of tests and experiments on several prototypes of key design features will be presented and discussed.
Poster 2: 17
The Recent Improvements of the SNS Extraction Kicker Power Supplies
Oak Ridge National Laboratory, United States of America
A total of 14 extraction kickers, with one as the hot spare, are in service to extract protons out of the storage ring at SNS. The jitter issue and the short lifetime of the switches were resolved after the thyratrons were replaced with solid state switches in 2018. This paper discusses the recent improvements. Two thyristor switches suffered overheating damage in separate incidents. One was due to the oil pump failure and the other was the result of a disconnected oil hose. An ultrasonic flow meter and fiber optic temperature monitors have been installed for each extraction kicker power supply. The flow meter continuously monitors the entire tank oil flow. The temperature monitors detect the thyristor switch real-time temperatures in three locations. Fault thresholds are selected so that the thyristor switches are protected from overheating damage. Alarms are configured to alert staff to take actions before faults occurs. In addition, the cause of an intermittent mis-fire issue was identified, and the solution was implemented. Lastly, a future oscilloscope upgrade is discussed.
Poster 2: 18
Los Alamos National Laboratory Fast Kicker Upgrade 2022
Los Alamos National Laboratory, United States of America
Approved for public release; distribution is unlimited.
The Los Alamos Neutron Science Center’s proton storage ring (PSR) extraction kicker systems consist of two thyratron switched blumlein modulators. The operating parameters of the PSR have changed over the years and the flattop voltage of the modulator outputs has become a limiting factor in the length of the beam pulse able to be extracted from the ring. The extraction voltage pulse travels upstream relative to the beam and thus needs to be longer than the beam pulse. A reanalysis of the voltage waveforms and the beam propagation times revealed that a longer pulse could reduce beam spill levels that have been seen during past run cycles. Reduced spill will allow operation at higher beam currents and thus increase the amount of beam current available for experimenters. We have upgraded the blumlein cables in both extraction kicker modulators with longer cables. We present test results of the modulator outputs and correlate their improvement with reduced beam losses at the PSR exit septum and improved beam delivery.
Poster 2: 19
Fast Measurements with Modified HVD Series of High Voltage Dividers
Spellman High Voltage Electronics Corp., United States of America
HVD Series of precision high voltage dividers manufactured by Spellman  are specified for DC measurements only. As such, they possess very high input impedance (1 GOhm and higher) and are corona-free.
We modified 100‑kV and 200‑kV models for time-domain measurements, extending the range of HVD100 to 140 kV. These models are dubbed HVD100C, HVd140C, and HVD200C (C stands for “compensated”). The last two models have also modified corona suppression electrodes, and E-field analysis is described showing that the field is below corona inception. Typical usable risetime is 2 us for 100‑kV and 140‑kV models, and 10 us for the 200‑kV kV model. Settling time to 0.2 % is less than 2 ms.
HVDs are calibrated for fast response both at low and high voltage by step response method; calibration results are provided. The modified, compensated, versions retain the same DC accuracy as their original DC counterparts.
The modified HVDs are useful for laboratory and manufacturing practices when HV time domain measurements are necessary in combination with high DC accuracy and high input impedance.
 Resistive Voltage Dividers, https://www.spellmanhv.com/en/high-voltage-power-supplies/HVD
Poster 2: 20
A Multi-Hundred kW HV Power Supply Platform with Low Stored Energy for Industrial Applications
Spellman High Voltage Electronics Corp., United States of America
A modular concept and industrialized demonstration of a 200kW, 45kV power supply possessing high dynamic characteristics is described. The system is comprised of eight 25kW, 45kV chassis connected in parallel and a control unit. Owing to the phase shift within and between the modules, high conversion frequency, and straight rectification schemes, the output capacitance is extremely low, which facilitates fast dynamic response, e.g., fast recovery after load sparking; stored energy is <10J, and ripple is <1% at full load.
The system is housed in three cabinets. Each chassis is packaged in a 19” 6U rack and weighs 45kg. Solid insulation and air cooling were adopted. Mechanical and electrical designs were assisted by circuit and FEA analyses. Particular attention, in view of high-power density, was paid to heat transfer, which was analyzed from the component level up to CFD modeling at the chassis and cabinet levels.
A variable parameter PID regulator achieves 300us rise time for a full range of loads without over/undershoots.
Poster 2: 21
Electric Field Driven Ionization Waves in Nanosecond-pulse Discharge
1Institute of Electrical Engineering, Chinese Academy of Sciences, China, People's Republic of; 2University of Chinese Academy of Sciences
Electric field is an extremely important microscopic parameter in the subject of high voltage (HV) and gas discharge. In this paper, electric field induced second harmonic (E-FISH), as a non-intrusive diagnostic method for electric field, is developed with good temporal and spatial evolution. This method is adopted to measure the spatial-temporal distribution of electric field in nanosecond pulsed discharges, including surface dielectric barrier discharge (SDBD)  and atmospheric pressure plasma jet (APPJ) , which verifies its reliability and feasibility. It is found that ionization waves (IWs) exist universally in nanosecond-pulse discharges with different geometries, which are driven by the intensified electric field at the wave front region. The weak electric field in the plasma channel is also very important for sustaining the IW propagation. Both space charges in surface and volume charges on dielectric will contribute to the measured electric field, the former of which generate a retarding electric field when IW propagates driven by unipolar HV pulses. To summery, the E-FISH diagnostic is a promising method to measure the space electric field and to retrace the behavior of space charges in a wider field of applications.
Poster 2: 22
Calculations of pulsed magnetic Field Interactions with Neurons using Sim4Life
1Purdue University, United States of America; 2Veritas Alchemy LLC; 3Luna Innovations
As medical applications of electromagnetic radiation transition from in vitro tests to the clinic, understanding multiscale behavior from the molecular to organism level becomes critical. This necessitates accurately modeling the interaction of electric fields at not only the cellular level, but at the tissue level. While many studies have investigated mechanisms at the cellular level, modeling in vivo effects requires determining the interaction of an applied electric field with the tissue before predicting cellular behavior . However, it can be difficult to ascertain how the different components in these systems will interact as they are vastly complicated compared to the single cell models explored already. This is even the case when considering something as apparently simple as dielectric properties, which will vary with tissue type and location throughout the body. Sim4Life (https://zmt.swiss/sim4life) is a multiphysics software that was specifically developed to perform these calculations from the electromagnetic source to the tissue level by considering the physical and dielectric properties of phantoms for an organism of interest. Furthermore, Sim4Life contains the functionality of integrating NEURON, which is an open source software that specifically assess the effect of an electric stimulus on neurons . This integrated software provides the user the flexibility to characterize changes in neuron behavior, such as action potentials, from an electromagnetic stimulus.
As a first step in this process, we are modeling the interaction of a pulsed magnetic field (PMF) applied to a rat model using Sim4Life. We will specifically consider the effects of pulse duration, rise- and fall-times, and repetition rates of the current source used to generate the PMF under the idea that the magnetic field will induce an electric field that will change the transmembrane potential of the exposed cells . Whether permeabilization is induced, we will be able to use the integrated Sim4Life and NEURON software to explore changes in the action potential for various PMF exposures, delivery mechanisms, and positions along the rat. Modifications of this model to assess ex vivo proof of principle experiments to benchmark the model prior to using it to guide in vivo tests on rats will be discussed.
This research was funded by the Defense Health Agency under contract #W81XWH-20-C-0094.
 D. Sel, et al., “Sequential finite element model of tissue electropermeabilization,” IEEE
Trans. Biomed. Eng., vol. 52, pp 816-827, 2005.
 M. L. Hines and N. T. Carnevale, “The NEURON simulation environment,” Neural
Comput., vol. 9, pp. 1179-1209, 1997.
 Q. Hu, R. P. Joshi, and D. Miklavčič, “Calculations of cell transmembrane voltage induced by
time-varying magnetic fields,” IEEE Trans. Plasma Sci., vol. 48, pp. 1088-1095, 2020.
Poster 2: 23
Modeling Plasma Membrane Pore Dynamics During Exposure to Electric Pulses Delivered by a Mismatched Blumlein Transmission Line
1Purdue University, United States of America; 2Texas Tech University, United States of America
Electroporation occurs in cells when an applied electric pulse (EP) induces a transmembrane potential above a threshold to cause an increase in the plasma membrane conductivity. Many experiments, mathematical models based on the Smoluchowski equation (SME), and molecular dynamics simulations have examined the phenomena responsible for this behavior for standard rectangular or trapezoidal waveforms. In practical experiments, the applied waveforms differ from these idealized shapes, particularly when applying multiple EPs that permeabilize the cells and cause ion transport between the cytoplasm and extracellular fluid that causes a mismatch between the impedance of the cell suspension and the pulse generator. For the Blumlein generators often used for nanosecond EP delivery, these mismatches can create fluctuations in the pulse waveforms, including periodic waves after the main rectangular EP . While important for applications involving multiple EP delivery, pore dynamics for a sinusoidal electric field after a rectangular EP have not been commonly studied. One study used the asymptotic SME to show that applying an AC field immediately after a square pulse could extend pore lifetime if it induced a sufficient amplitude of the transmembrane potential . This then raises the question about the implications of mismatch-induced sinusoidal electric field following the applied rectangular pulse on membrane pore dynamics, particularly depending on the frequency and intensity of this sinusoidal component. This presentation examines this behavior by applying an asymptotic Smoluchowski equation (SME)  to model membrane pore dynamics for a cell exposed to EP waveforms characteristic of these mismatches. We will examine the effects of the frequency and amplitude of the secondary sinusoidal electric fields on membrane pore dynamics for main EPs of various rise- and fall-times, pulse durations, and electric field. We will also compare the results from this model to a simplified electroporation model based on transmembrane potential and assess potential intracellular effects that may arise due to these more realistic pulse waveforms.
 J.F. Kolb, S. Kono, and K. H. Schoenbach, “Nanosecond pulsed electric field generators for the study of subcellular effects,” Bioelectromagnetics, vol. 27, pp. 172-187, 2006.
 A. L. Garner and V. B. Neculaes, “Extending membrane pore lifetime with AC fields: A modeling study,” J. Appl. Phys., vol. 112, 2012, Art. no. 014701.
 S. Talele, P. Gaynor, M. J. Cree, and J. van Ekeran, “Modelling single cell electroporation with bipolar pulse parameters and dynamic pore radii,” J. Electrostatics, vol. 68, pp. 261-274, 2010.
This research was funded by the Office of Naval Research under grant #N00014-21-1-2055 and the Defense Health Agency under contract #W81XWH-20-C-0094.