JOURNAL OF LATEX CLASS FILES 1 A Primer on Pulsed Power and Linear Transformer Drivers for High Energy Density Physics Applications R. D. McBride, Member, IEEE, W. A. Stygar, Member, IEEE, M. E. Cuneo, Fellow, IEEE, D. B. Sinars, Senior Member, IEEE, M. G. Mazarakis, Life Member, IEEE, J. J. Leckbee, Member, IEEE, M. E. Savage, Member, IEEE, B. T. Hutsel, Member, IEEE, J. D. Douglass, Member, IEEE, M. L. Kiefer, B. V. Oliver, Fellow, IEEE, G. R. Laity, Member, IEEE, M. R. Gomez, Member, IEEE, D. A. Yager-Elorriaga, Member, IEEE, S. G. Patel, Member, IEEE, B. M. Kovalchuk, A. A. Kim, P.-A. Gourdain, S. N. Bland, Member, IEEE, S. Portillo, Member, IEEE, S. C. Bott-Suzuki, Member, IEEE, F. N. Beg, Fellow, IEEE, Y. Maron, Fellow, IEEE, R. B. Spielman, Member, IEEE, D. V. Rose, D. R. Welch, Member, IEEE, J. C. Zier, J. W. Schumer, Senior Member, IEEE, J. B. Greenly, A. M. Covington, A. M. Steiner, Member, IEEE, P. C. Campbell, Member, IEEE, S. M. Miller, Member, IEEE, J. M. Woolstrum, Member, IEEE, N. B. Ramey, Member, IEEE, A. P. Shah, B. J. Sporer, N. M. Jordan, Member, IEEE, Y. Y. Lau, Fellow, IEEE, and R. M. Gilgenbach, Life Fellow, IEEE (Invited Paper) Abstract—The objectives of this tutorial are as follows: (1) Manuscript received February 2, 2018; revised July 19, 2018; accepted to help students and researchers develop a basic understanding September 4, 2018. This work was supported in part by the U.S. Nuclear Reg- of how pulsed-power systems are used to create high-energy- ulatory Commission through a faculty development grant, in part by the NSF density matter; (2) to develop a basic understanding of a new, through the NSF-DOE Partnership in Basic Plasma Science and Engineering compact, and efficient pulsed-power technology called Linear under Grant PHY-1705418, in part by the NNSA within the DOE through the SSAA Program under Cooperative Agreement DE-NA0003764, and in part Transformer Drivers (LTDs); (3) to understand why LTDs are by Sandia National Laboratories through the LDRD and Campus Executives an attractive technology for driving HEDP experiments; (4) to Programs under Project 20-9240. Sandia is a multimission laboratory managed contrast LTDs with the more traditional Marx-generator/pulse- and operated by National Technology and Engineering Solutions of Sandia, forming-line approach to driving HEDP experiments; and (5) to LLC., a wholly owned subsidiary of Honeywell International, Inc., for the briefly review the history of LTD technology as well as some of the U.S. DOE’s NNSA under contract DE-NA0003525. LTD-driven HEDP research presently underway at universities R. D. McBride, P. C. Campbell, S. M. Miller, J. M. Woolstrum, and research laboratories across the globe. This invited tutorial N. B. Ramey, A. P. Shah, B. J. Sporer, N. M. Jordan, Y. Y. Lau, and is part of the Mini-Course on Charged Particle Beams and R. M. Gilgenbach are with the Department of Nuclear Engineering and High-Powered Pulsed Sources, held in conjunction with the 44th Radiological Sciences at the University of Michigan, Ann Arbor, MI 48109 USA; e-mail: [email protected] (see https://plasmabay.engin.umich.edu/). International Conference on Plasma Science in May of 2017. W. A. Stygar, M. E. Cuneo, D. B. Sinars, M. G. Mazarakis, J. J. Leckbee, Index Terms—linear transformer driver, LTD, high-energy- M. E. Savage, B. T. Hutsel, J. D. Douglass, M. L. Kiefer, B. V. Oliver, density physics, HEDP, pulsed power, magnetized liner iner- G. R. Laity, M. R. Gomez, D. A. Yager-Elorriaga, and S. G. Patel are with tial fusion, MagLIF, inertial confinement fusion, ICF, material Sandia National Laboratories, Albuquerque, NM 87185 USA. B. M. Kovalchuk and A. A. Kim are with the Institute of High Current properties, equation of state, radiation sources, radiation effects, Electronics, Russian Academy of Sciences, Tomsk 634055 Russia radiation science, laboratory astrophysics. P.-A. Gourdain is with the Extreme State Physics Laboratory, Department of Physics and Astronomy, University of Rochester, NY 14627 USA. S. N. Bland is with the Blackett Laboratory, Physics Department, Imperial I. INTRODUCTION College, London SW7 2BW United Kingdom. S. Portillo is with the University of New Mexico, Albuquerque, NM 87131 IGH-ENERGY-DENSITY PHYSICS (HEDP) is defined USA. H as the study of matter and radiation at extreme condi- S. C. Bott-Suzuki and F. N. Beg are with the University of California, San tions, where the energy density is about 1011 J/m3 or higher. Diego, CA 92093 USA. Y. Maron is with the Weizmann Institute of Science, Faculty of Physics, Noting that the units of pressure are the units of energy Rehovot 76100 Israel. density (i.e., 1 Pa = 1 N/m2 = 1 kg/(m·s2) = 1 J/m3), HEDP R. B. Spielman is with the Idaho State University, Pocatello, ID 83209 material pressures are often at or above 1 Mbar (≈ 1 mil- USA. D. V. Rose and D. R. Welch are with Voss Scientific, LLC, Albuquerque, lion atmospheres). To drive matter to such an extraordinary NM 87108 USA. state requires a high-power, high-energy, high-pressure driver J. C. Zier and J. W. Schumer are with the Naval Research Laboratory, system. These systems often come in the form of large pulsed- Washington, DC 20375 USA. J. B. Greenly is with the Laboratory of Plasma Studies, Cornell University, power facilities or large laser facilities. Present state-of-the-art Ithaca, NY 14853 USA. HEDP facilities include the Z pulsed-power facility at Sandia A. M. Covington is with the Nevada Terawatt Facility, Department of National Laboratories [1], [2], the OMEGA and OMEGA-EP Physics, University of Nevada, Reno, NV 89557 USA. A. M. Steiner is currently with Lockheed Martin Aeronautics “Skunk laser facilities at the University of Rochester’s Laboratory for Works,” Palmdale, CA 93599, USA. Laser Energetics [3], [4], and the National Ignition Facility JOURNAL OF LATEX CLASS FILES 2 (NIF) at Lawrence Livermore National Laboratory [5], [6]. brass, copper, and gold. On 100-ns time scales, these materials These facilities support a variety of programs in stockpile have skin depths stewardship and basic science. For example, the pulsed-power r 4ρeτr facilities at Sandia presently support stockpile stewardship δskin = ∼ 100 µm; (2) experiments in inertial confinement fusion (ICF) [7]–[10], πµ0 material properties [11], [12], radiation physics [13], [14], where ρe ∼ 100 nΩ·m is the electrical resistivity of the metal radiation effects testing [15], [16], and advanced radiography electrodes, τr ∼ 100 ns is the rise time of the driving current −7 development [17], [18] as well as basic science programs pulse, and µ0 = 4π × 10 H/m is the permeability of free in material properties [19], radiation physics [20], planetary space. In contrast with δskin ∼ 100 µm, the anode-cathode science [21], and laboratory astrophysics [22]. gaps and imploding cylindrical targets in pulsed-power-driven In this tutorial, we will focus solely on pulsed-power HEDP experiments typically have spatial dimensions ∼ 1 cm. technology for driving HEDP experiments. We will first Thus, the current pulse I(t) is indeed a surface current, and establish a basic, general picture of a pulsed-power-driven the perfectly conducting electrode assumption is reasonable. HEDP experiment. We will then use this picture to understand Because of the cylindrical symmetry assumption, the zero a relatively new pulsed-power technology for HEDP called initial field assumption, and the perfect conductor assumption, Linear Transformer Drivers (LTDs) [23]–[38]. To provide the magnetic field generated by the rising current pulse is a basis for comparison, we will also briefly describe the purely an azimuthal field that exists only in the vacuum regions more traditional Marx-generator/pulse-forming-line approach of the cavity (i.e., this field is excluded from the metal regions). to driving HEDP experiments. As we will see, LTDs offer This field can be represented in the vacuum region as compact, efficient, and fully enclosed packaging of the pulsed- µ0I power components (e.g., capacitors and switches) as well as B = B (r) θ^ = θ^: (3) θ 2πr a highly modular design to enable the construction of large LTD-based systems. Finally, we will briefly review the LTD’s This expression can be understood with the help of Fig. 2. history and provide some examples of recent LTD-driven Because of the perfect conductor boundary condition, we know HEDP research from across the globe. It is our hope that from fundamental electricity and magnetism that the surface the picture of pulsed-power-driven HEDP presented in this current density Js (a linear current density in units of A/m tutorial will complement the pictures presented previously in running along the metal surface) is essentially equivalent to the other similar review articles (e.g., Ref. [39]). value of the tangential magnetic field B at the metal surface (the equivalence is given through the proportionality constant µ0, which is the magnetic permeability of free space—see II. A SIMPLE PICTURE OF A PULSED-POWER-DRIVEN Fig. 2). Additionally, we must keep in mind that for perfect HEDP EXPERIMENT conductors, the direction of the surface current density is In its simplest form, a basic pulsed-power driven HEDP perpendicular to the direction of the magnetic field at the metal experiment begins with a cylindrically symmetric, vacuum- surface (Js ? B) and that both Js and B have only tangential filled, metal cavity (see Fig. 1(a)). Around the perimeter of components (their components normal to the metal surfaces this cavity, we want to apply a large voltage V in order to are zero everywhere). Putting this all together, we have drive a very fast rising, high amplitude current pulse I(t).