Pulsed Power Accelerator Research Articles

Method to determine the optimal impedance profile of nonuniform transmission lines used for pulsed power accelerators

Nonuniform transmission lines (NTLs) are widely used in pulsed power accelerators because they provide an efficient way to achieve impedance matching and pulse shaping. Since designing and constructing these accelerators typically demands substantial effort, finding the optimal impedance profile to maximize the power transmission efficiencies of the NTLs is important. In this paper, a convenient numerical method to determine the optimal impedance profile is proposed. First, the output of the NTL with arbitrary parameters is theoretically analyzed under arbitrary input conditions. It was found that only four factors affect the power transmission efficiency: the ratio of output impedance to input impedance, the ratio of input pulse width to the NTL’s one-way transit time, the normalized impedance profile, and the normalized input pulse. Based on these findings, a method designed to minimize the reflected component within the working frequency range is proposed. Using this method, an impedance profile demonstrating superior power transmission efficiency compared to the traditional exponential profile is identified. This work can provide a rapid and effective method to determine the impedance profile of the NTL, undoubtedly benefiting the design process of pulsed power accelerators. Published by the American Physical Society 2024

Profile of Inner Magnetically Insulated Transmission Lines to Minimize Energy Loss Under MA/Cm Lineal Current Density for High-Current Pulsed-Power Accelerators

Profile of Inner Magnetically Insulated Transmission Lines to Minimize Energy Loss Under MA/Cm Lineal Current Density for High-Current Pulsed-Power Accelerators

The numerical simulation of a four-stage linear transformer driver module based on the Preisach magnetic core model.

The use of linear transformer drivers (LTDs) is widely considered the most promising technological approach for the development of future pulsed-power accelerators. In large-scale pulsed-power accelerators, abnormal conditions like switch prefire can occur frequently during tests and normal operations due to the presence of a large number of switches. The diagnosis of such faults based on signature waveforms requires further investigation. According to previous research, the characteristics of the magnetic cores greatly influence the fault waveforms. In this paper, a full-cycle mathematical model of the magnetic core is established utilizing a classical Preisach model based on experimental results. This model is coupled with the LTD circuit model in simulations, and simulation results are obtained under the condition of switch prefire. The simulation results are in good agreement with the experimental results from a four-stage LTD module with a sharing shell and de-ionized water insulated transmission line. The magnetization process of the cores is also determined under prefire conditions. Analyses of the magnetization process indicate that the completely demagnetized core shows high permeability under positive excitation and that the permeability abruptly decreases as the excitation is reversed. The hysteresis characteristics result in a phenomenon in which the output voltage in the prefired stage is almost unipolar. Finally, the features of the fault voltages captured in the experiments are also explained.

Magneto-optical measurement of magnetic field and electrical current on a short pulse high energy pulsed power accelerator

We describe a direct magneto-optical approach to measuring the magnetic field driven by a narrow pulse width (<10 ns), 20 kA electrical current flow in the transmission line of a high energy pulsed power accelerator. The magnetic field and electrical current are among the most important operating parameters in a pulsed power accelerator and are critical to understanding the properties of the radiation output. However, accurately measuring these fields and electrical currents using conventional pulsed power diagnostics is difficult due to the strength of ionizing radiation and electromagnetic interference. Our approach uses a fiber coupled laser beam with a rare earth element sensing crystal sensor that is highly resistant to electromagnetic interference and does not require external calibration. Here, we focus on device theory, operating parameters, results from an experiment on a high energy pulsed power accelerator, and comparison to a conventional electrical current shunt sensor.

Electrode plasma formation and melt in Z -pinch accelerators

Recent studies of power flow and particle transport in multi-MA pulsed-power accelerators demonstrate that electrode plasmas may reduce accelerator efficiency by shunting current upstream from the load [Bennett et al., Phys. Rev. Accel. Beams 24, 060401 (2021)]. The detailed generation and evolution of these electrode plasmas are examined here using fully relativistic, Monte Carlo particle-in-cell (PIC) and magnetohydrodynamic (MHD) simulations over a range of peak currents (8--48 MA). The PIC calculations, informed by vacuum science, describe the electrode surface breakdown and particle transport prior to electrode melt. The MHD calculations show the bulk electrode evolution during melt. The physical description provided by this combined study begins with the rising local magnetic field that increases the local electrode surface temperature. This initiates the thermal desorption of contaminants from the electrode surface, with contributions from atoms outgassing from the bulk metal. The contaminants rapidly ionize forming a ${10}^{15}--{10}^{18}\text{ }\text{ }{\mathrm{cm}}^{\ensuremath{-}3}$ plasma that is effectively resistive while weakly collisional because it is created within, and rapidly penetrated by, a strong magnetic field ($>30\text{ }\text{ }\mathrm{T}$). Prior to melting, the density of this surface plasma is limited by the concentration of absorbed contaminants in the bulk ($\ensuremath{\sim}{10}^{19}\text{ }\text{ }{\mathrm{cm}}^{\ensuremath{-}3}$ for hydrogen), its diffusion, and ionization. Eventually, the melting electrodes form a conducting plasma (${10}^{21}--{10}^{23}\text{ }\text{ }{\mathrm{cm}}^{\ensuremath{-}3}$) that experiences $\mathbf{j}\ifmmode\times\else\texttimes\fi{}\mathbf{B}$ compression and a typical decaying magnetic diffusion profile. This physical sequence ignores the transport of collisional plasmas of ${10}^{19}\text{ }\text{ }{\mathrm{cm}}^{\ensuremath{-}3}$ which may arise from electrode defects and associated instabilities. Nonetheless, this picture of plasma formation and melt may be extrapolated to higher-energy pulsed-power systems.

Characteristics of the D-Dot Sensor for Measurement of High Voltage Pulse of a Water-Insulated Transmission Line

The characteristics of the differential-output D-dot sensor, which is employed to diagnose the voltage pulse across the water-insulated component of the pulsed power accelerator, are investigated by theory, circuit simulation, and experiments. The leakage current from the D-dot sensor to the inner electrode of the measured component will degrade the low-frequency response property of the monitor. The lower level of the water medium resistivity the worse performance of the sensor’s low-frequency response property will be. The actual lower-limited response frequency of the D-dot sensor is not related to the sensor itself but is mainly determined by the resistivity of the water. These are not only deduced from theory but also approved by the experimental results. Circuit simulation results suggest that the D-dot sensor without consideration of the leakage current will over-evaluate the amplitude and rise time of the voltage pulse across the water-filled element. We have proposed a method to make compensation for such an effect by using a passive resistor–capacitor (RC) integrator instead of the numerical process suggested previously. It is approved both by circuit simulation and experimental results that the output of the D-dot sensor post-processed by the RC integrator could give accurate measurement results providing that the time constant of the RC integrator is identical to the characteristic time of the D-dot sensor.

Observation and diagnostic application of Kr K-shell emission in magnetized liner inertial fusion experiments at Z.

In a series of Magnetized Liner Inertial Fusion (MagLIF) experiments performed at the Z pulsed power accelerator of Sandia National Laboratories, beryllium liners filled with deuterium gas pressures in the 4-8 atm range and a tracer amount of krypton were imploded. At the collapse of the cylindrical implosion, temperatures in the 1-3keV range and atom number densities of ∼1023 cm-3 were expected. The plasma was magnetized with a 10T axial magnetic field. Krypton was added to the fuel for diagnosing implosion plasma conditions. Krypton K-shell line emission was recorded with the CRITR time-integrated transmission crystal x-ray spectrometer. The observation shows n = 2 to n = 1 line emissions in B-, Be-, Li-, and He-like Kr ions and is characteristic of the highest electron temperatures achieved in the thermonuclear plasma. Detailed modeling of the krypton atomic kinetics and radiation physics permits us to interpret the composite spectral feature, and it demonstrates that the spectrum is temperature sensitive. We discuss temperatures extracted from the krypton data analysis for experiments performed with several filling pressures.

Characteristics of Switch Prefire Generated Fault Voltages Transmitted in a Four-Stage LTD Module

Future large-scale pulsed-power accelerators are commonly designed based on linear transformer driver (LTD) topology. With the number of gas switches being significant (~ 100000), gas switch prefire might be an inevitable malfunction in an LTD accelerator. The transmission characteristics of switch prefire and its influences on major components in a multicavity LTD module remain to be investigated. In this article, the mechanism of fault voltage generation by switch prefire and inductive coupling effect of the magnetic core were thoroughly understood. It was found that switch prefire drove the cores to magnetize reversely toward negative saturation state ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$- B_{s}$ </tex-math></inline-formula> ), raising the voltage on switches in adjacent stages. A circuit model reflecting both initial states and magnetization dynamics of cores was developed for numerical analysis of switch prefire. From previous tests of a four-stage LTD module with deionized water insulated transmission line, unexpected discharges were captured and recognized by D-dots installed in the internal electrode of the transmission line. Test results indicated that an evident manifestation of switch prefire was the polarity reversion of D-dot voltage pulses. Both theoretical and experimental analyses revealed that single brick prefire generated a peak voltage of 70 kV across the transmission line under the charge voltage of ±70 kV. Circuit simulations were in good accordance with experimental data of D-dot signals in the main pulse. However, discrepancies between simulations and experimental results implied that the model was not precise enough in the magnetization dynamics under saturated state.

Dynamics of the super pinch electron beam and fusion energy perspective

The characterization of a high current, relativistic electron beam, designated the Super Pinch electron beam, has been performed using compact pulsed-power accelerators of various architectures with a novel diode geometry. The Thunderbird accelerator has an initial $1.5\text{\ensuremath{-}}\ensuremath{\mu}\mathrm{s}$ rise time and 150-kA peak current. The drive voltage is compressed to produce a 12-ns 500-kV voltage pulse generating a $\ensuremath{\sim}40\text{\ensuremath{-}}\mathrm{kA}$ electron beam, which apparently exceeds the Alv\'en current limit although the useful current at small radius is an order of magnitude less. Using an insulated hollow cathode with a 0.5-cm anode-cathode gap, the large current is enabled by the evolution of plasma from the dielectric sleeve enveloping the cathode and a 0.5-mm wire anode. Post-shot recovery of the anode target and measurements of its deformation and damage allow an evaluation of the enhanced electron-beam focusing whereby significant beam energy is delivered to the record small, microscopic volume inside the anode target. The electron beam is seen to have conditions favorable to those needed to ignite compressed fuel in inertial confinement fusion. These results motivated a deeper insight using theoretical modeling with hybrid particle-in-cell codes. The modeling presented in this paper shows an electron beam radius of $&lt;10\text{ }\text{ }\ensuremath{\mu}\mathrm{m}$ containing a current of 3--6 kA or $&gt;500\text{ }\text{ }\mathrm{MA}/{\mathrm{cm}}^{2}$ current density. Scaling up the accelerator, such preferred focusing, target penetration, and affordability of the pulsed power generated electron beams open a new opportunity for the application of the mainstream pulsed power devices in the research and development of fusion energy.

Analytic Model and Optimization of Transmission-Line Impedance Transformers for Tens of MA-Class Pulsed Power Accelerator

The monolithic radial transmission line (MRTL) is a key component in tens of MA-class pulsed power accelerators, which connects the multiparallel modules of the prime pulsed power sources to the central vacuum insulator stack and magnetically insulated transmission line (stack-MITL system). The choice of electrical parameters of MRTL is essential for the entire accelerator design, which would bring great influences on the peak output current and the power couple efficiency. In Phys. Rev. Special Topics-Accel. Beam s, 2015, 18(10): 110401, some semianalytical formulae have been proposed to optimize the MRTL impedance that maximizes the peak current or peak power on the stack-MITL system. However, the formulae are only valid under several assumptions that are thought to be unpractical. In this article, an analytic model of the accelerator is developed to optimize the electrical parameters of MRTL. Analytical expressions of the output voltage and current at the terminal of MRTL are deduced. By simplifying the analytic model, mathematical expressions of the optimal MRTL output impedance that maximizes the peak current or peak power delivered from the prime power sources to the stack-MITL system are obtained. The factors that contribute to the optimal impedance are analyzed comprehensively with short-circuit load and Z-pinch load. Conclusions are beneficial to design the pulsed power accelerator in the future.

Frequency Response Properties of the B-Dot Sensors Employed on a High Current Pulsed Power Facility

B-dot sensor, as an important device, is extensively employed to measure the current flowing in the magnetically insulated transmission line (MITL). To shield the output signal of the B-dot sensor from electron flow and high electrical field in the MITL anode-cathode (A-K) gap and also avoid the electrical breakdown in the A-K gap, the sensor is often covered with the metallic film and located in a conductor cavity penetrating the MITL electrode hole simultaneously. The frequency response properties of such kind of sensor are investigated. The experiment results indicate that the upper limited response frequencies of the sensors with and without the attached 5-μ m-thick Ni-Chrome foil are 50 MHz and 148 MHz, respectively. Moreover, as a result of penetration of magnetic flux into the cavity's wall and the wire loops wound to form the sensor, the low-frequency components of the B-dot sensor output signal are amplified, consequently the falling edge of the waveform given by the B-dot probe will be distorted. We have proposed a method to make a first-order correction for such effect by using a passive resistor-capacitor integrator instead of the numerical process suggested previously. The integrator combines the behaviors of integration and compensation of the B-dot sensor output. The actual measured current waveform can be directly obtained by multiplying the output signal of the integrator by the sensitivity of the B-dot monitor. The B-dot sensors and this post-processing method have been successfully used on a pulsed power accelerator.

Electro-optical measurement of intense electric field on a high energy pulsed power accelerator

We describe a direct electro-optical approach to measuring a strong 118 MV/m narrow pulse width (~ 33 ns) electric field in the magnetically insulated transmission line (MITL) of a pulsed power accelerator. To date, this is the highest direct external electric field measured electro-optically in a pulsed power accelerator, and it is between two to three orders of magnitude higher than values reported in comparable high energy scientific experiments. The MITL electric field is one of the most important operating parameters in an accelerator and is critical to understanding the properties of the radiation output. However, accurately measuring these high fields using conventional pulsed power diagnostics is difficult due to the strength of interfering particles and fields. Our approach uses a free-space laser beam with a dielectric crystal sensor that is highly immune to electromagnetic interference and does not require an external calibration. Here we focus on device theory, operating parameters, laboratory and pulsed power accelerator experiments as well as challenges that were overcome in the measurement environment.

Miniature solid-state switched spiral generator for the cost effective, programmable triggering of large scale pulsed power accelerators

This paper presents the design and testing of several different configurations of spiral generator, designed to trigger high current switches in the next generation of pulsed power devices. In particular, it details the development of spiral generators that utilize new ultrafast thyristor technology as an input switch, along with a polarity dependent output gap to improve the efficiency of the spiral generator design. The generator produced 50 kV from a 3.6 kV charging voltage, with a rise time of only 50 ns and a jitter of 1.3 ns---directly comparable, if not better than, a generator employing a triggered spark gap as the input switch. The output gap was constructed in house from commonly available components and a 3D printed case, and showed remarkable repeatability and stability---simple alterations to the output gap could further reduce the rise time. The entire spiral generator, along with control and charging electronics, fitted into a case only $210\ifmmode\times\else\texttimes\fi{}145\ifmmode\times\else\texttimes\fi{}33\text{ }\text{ }\mathrm{mm}$.

Optical performance test and energy resolution analysis on LaBr3(Ce) crystal

The paper used 137Cs and 60Co γ sources to measure and analyze the effects of different voltage, gain, count time of photomultiplier tube and different distance of sources on the energy resolution of LaBr3(Ce) crystal; the relationship curves were obtained quantitatively. The experiment values are in good agreement with MCNP simulation results. The results show that the energy resolution of LaBr3(Ce) is negatively correlated with voltage and gain; the gain is more influential. The energy resolution of LaBr3(Ce) is positively correlated with detection distance and count time; the detection distance is more influential. The paper used picosecond X-ray generated by pulsed power accelerator “Qiangguang-?” to excite the LaBr3(Ce) crystal and measure its fluorescence decay time and emission spectrum. The results are consistent with the available experimental data of other scholars and verify the excellent time response of LaBr3(Ce). With the increase in X-ray energy, the peak emission wavelength shifts towards infrared direction, which can better match the spectral response of photocathode.

Fast hybrid particle-in-cell technique for pulsed-power accelerators

Hybrid-implicit particle-in-cell (PIC) algorithms permit the simulation of complex problems involving both kinetic and fluid plasma regimes over large spatial and temporal scales. Fluid electrons can be computationally fast where and when fluid assumptions are valid. Additional flexibility is obtained if discrete PIC macroparticles, with velocities advanced by either fluid or kinetic equations, are permitted to dynamically migrate between the two descriptions based on phase space criteria. Ideally, these migrations result in energetic particles treated kinetically and dense thermal plasma particles as a fluid. With an energy-conserving particle advance, resolution of the plasma Debye length is not required for numerical accuracy or stability. For pulsed-power applications, the simulation time step is usually constrained by the electron cyclotron frequency, not the more restrictive plasma frequency. A new implicit technique permits accurate particle orbits even at highly underresolved cyclotron frequencies. Thus, greater temporal and spatial scales can be accurately modeled relative to conventional PIC techniques. In this paper, we describe the hybrid PIC technique and fully electromagnetic, hybrid simulations of plasma evolution and current shunting in an idealized accelerator designed for driving a $Z$-pinch load. The dynamics of electrode heating, electron transport, and surface contaminant evolution are studied in a series of relativistic hybrid-implicit PIC simulations. These dynamics can lead to the shunting of current before reaching the $Z$-pinch load, thus degrading load performance. Examining two previously published power flow problems, we compare results from fully kinetic, multifluid, and hybrid kinetic-fluid simulations and discuss the computational performance of these three options. The key thrust of the work is to identify possible computational acceleration, through hybrid methods, required for accelerator understanding and design.

Pulsed power accelerator surface Joule heating models

Understanding the effects of contaminant plasmas generated within the Z machine at Sandia is critical to understanding current loss mechanisms. The plasmas are generated at the accelerator electrode surfaces and include desorbed species found in the surface and substrate of the walls. These desorbed species can become ionized. The timing and location of contaminant species desorbed from the wall surface depend non-linearly on the local surface temperature. For accurate modeling, it is necessary to utilize wall heating models to estimate the amount and timing of material desorption. One of these heating mechanisms is Joule heating. We propose several extended semi-analytic magnetic diffusion heating models for computing surface Joule heating and demonstrate their effects for several representative current histories. We quantitatively assess under what circumstances these extensions to classical formulas may provide a validatable improvement to the understanding of contaminant desorption timing.

Review of pulsed power-driven high energy density physics research on Z at Sandia

Pulsed power accelerators compress electrical energy in space and time to provide versatile experimental platforms for high energy density and inertial confinement fusion science. The 80-TW “Z” pulsed power facility at Sandia National Laboratories is the largest pulsed power device in the world today. Z discharges up to 22 MJ of energy stored in its capacitor banks into a current pulse that rises in 100 ns and peaks at a current as high as 30 MA in low-inductance cylindrical targets. Considerable progress has been made over the past 15 years in the use of pulsed power as a precision scientific tool. This paper reviews developments at Sandia in inertial confinement fusion, dynamic materials science, x-ray radiation science, and pulsed power engineering, with an emphasis on progress since a previous review of research on Z in Physics of Plasmas in 2005.

Investigating the influence of the wire-arrays’ electrical parameters on the load current of the z-pinch drivers

Wire arrays are the typical loads which have been widely used in z-pinch research studies. When a large pulsed power accelerator is designed, the electrical parameters of the z-pinch loads including the inductance and the resistance (or the equivalent resistance) must be considered. In this paper, the inductance and the resistance of the single planar wire arrays were introduced from the experiments carried out on a Qiangguang accelerator (1.5 MA, 100 ns). The lumped-element circuit model of the wire array was established using the PSPICE software, and the model was verified by comparing the simulation results with the experimental results. The influence of the electrical parameters on the accelerator’s driving current is investigated. It shows that the inductance affects the rising edge and the peak value of the current, while the resistance mainly affects the current waveform after the stagnation of the wire array pinch load. The inductance model based on the zero-dimensional equation is compared with the inductance model based on the experimental data, and the result shows that the two different inductance models give almost the same pinch current. It can be concluded that the zero-dimensional model is valid in circuit simulation to investigate the peak current of the designed z-pinch accelerator.

Conceptual design of a 15-TW pulsed-power accelerator for high-energy-density–physics experiments

We have developed a conceptual design of a 15-TW pulsed-power accelerator based on the linear-transformer-driver (LTD) architecture described by Stygar [W. A. Stygar et al., Phys. Rev. ST Accel. Beams 18, 110401 (2015)]. The driver will allow multiple, high-energy-density experiments per day in a university environment and, at the same time, will enable both fundamental and integrated experiments that are scalable to larger facilities. In this design, many individual energy storage units (bricks), each composed of two capacitors and one switch, directly drive the target load without additional pulse compression. Ten LTD modules in parallel drive the load. Each module consists of 16 LTD cavities connected in series, where each cavity is powered by 22 bricks connected in parallel. This design stores up to 2.75 MJ and delivers up to 15 TW in 100 ns to the constant-impedance, water-insulated radial transmission lines. The transmission lines in turn deliver a peak current as high as 12.5 MA to the physics load. To maximize its experimental value and flexibility, the accelerator is coupled to a modern, multibeam laser facility (four beams with up to 5 kJ in 10 ns and one beam with up to 2.6 kJ in 100 ps or less) that can provide auxiliary heating of the physics load. The lasers also enable advanced diagnostic techniques such as X-ray Thomson scattering and multiframe and three-dimensional radiography. The coupled accelerator-laser facility will be the first of its kind and be capable of conducting unprecedented high-energy-density–physics experiments.

Impedance-matched Marx generators

We have conceived a new class of prime-power sources for pulsed-power accelerators: impedance-matched Marx generators (IMGs). The fundamental building block of an IMG is a brick, which consists of two capacitors connected electrically in series with a single switch. An IMG comprises a single stage or several stages distributed axially and connected in series. Each stage is powered by a single brick or several bricks distributed azimuthally within the stage and connected in parallel. The stages of a multistage IMG drive an impedance-matched coaxial transmission line with a conical center conductor. When the stages are triggered sequentially to launch a coherent traveling wave along the coaxial line, the IMG achieves electromagnetic-power amplification by triggered emission of radiation. Hence a multistage IMG is a pulsed-power analogue of a laser. To illustrate the IMG approach to prime power, we have developed conceptual designs of two ten-stage IMGs with $LC$ time constants on the order of 100 ns. One design includes 20 bricks per stage, and delivers a peak electrical power of 1.05 TW to a matched-impedance $1.22\text{\ensuremath{-}}\ensuremath{\Omega}$ load. The design generates 113 kV per stage and has a maximum energy efficiency of 89%. The other design includes a single brick per stage, delivers 68 GW to a matched-impedance $19\text{\ensuremath{-}}\ensuremath{\Omega}$ load, generates 113 kV per stage, and has a maximum energy efficiency of 90%. For a given electrical-power-output time history, an IMG is less expensive and slightly more efficient than a linear transformer driver, since an IMG does not use ferromagnetic cores.