Auto-Magnetizing liners for Magnetized Inertial Fusion

Transcription

1 Auto-Magnetizing liners for Magnetized Inertial Fusion S. A. Slutz, C.A. Jennings, T.J. Awe, G.A. Shipley, B.T. Hutsel, and D.C. Lamppa Sandia National Laboratories, Albuquerque, New Mexico 87185, USA Abstract The MagLIF (Magnetized Liner Inertial Fusion) concept [S.A. Slutz et al. Phys. Plasmas 17, (2010)] has demonstrated fusion relevant plasma conditions [M.R. Gomez et al. Phys. Rev. Lett. 113, (2014)] on the Z accelerator using external field coils to magnetize the fuel before compression. We present a novel concept (AutoMag), which uses a composite liner with helical conduction paths separated by insulating material to provide fuel magnetization from the early part of the drive current, which by design rises slowly enough to avoid electrical breakdown of the insulators. Once the magnetization field is established the drive current rises more quickly, which causes the insulators to break down allowing the drive current to follow an axial path and implode the liner in the conventional z-pinch manner. There are two important advantages to AutoMag over external field coils for the operation of MagLIF. Low inductance magnetically insulated power feeds can be used to increase the drive current and AutoMag does not interfere with diagnostic access. Also, AutoMag enables a pathway to energy applications for MagLIF, since expensive field coils will not be damaged each shot. Finally, it should be possible to generate Field Reversed Configurations (FRC) by using both external field coils and AutoMag in opposite polarities. This would provide a means to studying FRC liner implosions on the 100 ns time scale. I. Introduction The conventional approach to inertial confinement fusion (ICF) relies on implosion velocities greater than 350 km/s and spherical convergence of more than 30 to achieve the high fuel temperatures (T > 4 kev) and areal densities (ρr > 0.3 g/cm 2 ) required for ignition 1. Another approach is to use the magnetic pressure generated by pulsed-power accelerators to directly drive implosions. In this approach 5-10% of the stored energy can be converted to the implosion energy of a metal tube (liner), but with implosion velocities of only km/s when the liner thickness is sufficient to eliminate feed through of hydrodynamic instabilities. Magneto-inertial fusion (MIF) concepts can significantly relax the implosion velocity requirements of traditional ICF, while still achieving high temperatures by magnetizing the fuel. This initial seed field, which increases considerably during the liner implosion, decreases thermal conductivity normal to the field during fuel compression and increases fusion product confinement at stagnation 2-3. MagLIF 4-6 is a specific MIF concept, which is being studied at the Z facility. The three important stages of this concept are magnetization; laser preheating, and then compression of the fuel. The latter process is accomplished by using magnetic pressure provided by a pulsed-power machine to implode a metal liner onto the fuel. 1

2 Experiments integrating all three phases of the MagLIF concept have been performed on the Z accelerator 7-8, which validate the basic physics underlying the concept. Deuterium-deuterium (DD) neutron yields up to 3x10 12 (measured by activation and time of flight techniques 9-10 ) and deuterium plasma temperatures of kev (measured both by neutron time of flight and x-ray spectroscopy 11 ) have been obtained. In addition, secondary deuterium-tritium (DT) neutrons, a result of the tritons produced in the aneutronic branch of the DD reaction, were measured with yields up to 5x10 10, which indicates a high degree of magnetization of the stagnated fuel 12. So far the fuel magnetization has been accomplished with a system using a capacitor bank to drive external Helmholtz-like field coils 13, which is referred to as ABZ (Applied-B on Z). The field coils are shown schematically in Fig. 1. Although, this has been a practical means of demonstrating the concept there are some drawbacks. First, the external field coil approach is not energetically efficient. The field coils generate a strong field over a volume much larger than the liner, as can be seen in Fig 1. The total magnetic energy at peak magnetic field is 100s of kj, while the field energy within the liner is only about 100 J. Furthermore, to insure field uniformity in the fuel, the liner is placed at the center of the field coils, which requires an extension of the power feeds. This adds about 2.6 nh of inductance, which lowers the peak drive current that can be delivered by about 4 MA. In addition, diagnostic access is limited by the field coils for magnetization fields above 10 T. Figure 2a illustrates the geometry of the field coils, the liner, and the electrical feeds that deliver current to the MagLIF liner. Field coils are located above and below the liner, which maintains radial x-ray diagnostic access between the coils. However, the two field coils must be brought together 13 as illustrated in Fig. 2b to generate the high field strength (>30 Tesla 14 ) needed for maximum yield. This removes radial diagnostic access, which is critically important to the study, understanding and continued advancement of the MagLIF operation. An AutoMag liner consists of helical conduction paths separated by insulating material. During the early part of the current pulse, the drive current flows along the helical conducting paths to generate fuel magnetization thus eliminating the need for external field coils. The three phases of the AutoMag concept are described in section II. Two applications of AutoMag are described in section III and conclusions are given in section IV. II. The AutoMag concept 2

3 A. The magnetization phase The geometry of the AutoMag concept is illustrated in Fig 3a. A composite liner is composed of a conducting material in a helical pattern separated by an insulating layer. Here we show a beryllium liner with helical cuts, which are then filled with an insulating material (not shown) such as epoxy. Other fabrication approaches could be used. The current from the pulsed power machine flows helically through the conducting beryllium between the anode and cathode. The cuts have a slope over the bulk of the liner forcing the current to have an azimuthal component, which will generate an axial magnetic field both inside (B zi ) and outside (B zo ) of the liner. In this example the cuts are vertical near the ends of the liner so that the current flows in the purely axial direction, which does not generate an axial magnetic field and allows the field lines inside the liner to more smoothly connect to the field lines outside. We have included this section of straight cuts for generality, but numerical field simulations indicate they may not be necessary, e.g. Fig. 6. An example field line is shown schematically in Fig. 3a. We shall refer to the sections of beryllium as wires since they carry the current. The cross section of these wires is rectangular as illustrated in Fig. 3b, but could be a more rounded shape to delay the electrical breakdown within the insulating material. Assuming n wires, the azimuthal spacing is 2 r/n and the vertical spacing is 2 rtan( )/n so the azimuthal current/length is I/(2 rtan( )). Integrating Ampere s law over the rectangular path shown in Fig. 3b we obtain B zi + B zo = 0 I/(2 rtan( )) near the midplane, where B zi is the axial field within the liner and B zo is the field outside of the liner. We have assumed that the liner is long enough that end effects can be neglected and thus the radial component of the B-field can be neglected. Note that the field inside the liner, B zi, is essentially independent of the radial coordinate as is the field outside of the since the azimuthal current contained within the contour does not depend on either r ci or r co. Using flux conservation, we obtain tan eq. 1, where r L is the radius of the liner, and r R is the radius of the return current electrode. Equation 1 indicates that a 0.6 MA current will produce a 30 Tesla field assuming r L = 3 mm, r R =6 mm, = 45 degrees. This modest current could be produced early in the drive pulse produced by Z as indicated in Fig. 4. Note that the inductance of an AutoMag liner is increased by about 0.6 nh when = 45 degrees, but this only affects the early part of the drive current before the insulating material breaks down. 3

4 Equation 1 will be valid until the insulating material separating the wires undergoes electrical break down. Good insulating materials such as plastic or epoxy break down at electric field strengths greater than E BD ~ 1.5x10 7 V/m. An electric field will be produced within the insulators by both resistive and inductive effects. Although the beryllium wire is highly conductive there will be a voltage drop due to resistance. The resistive electric field along the liner is E R = IR/L, where L is the liner length. The resistance is given by R= E L/A, where E = 3.5x10-10 m is the electrical resistivity of beryllium, and A is the current carrying cross-sectional area given by A=4 r L f con, where / is the resistive skin depth, is the current rise-time during the magnetization phase, and f con is the metal volume fraction of the liner. / eq. 2 Assuming r L = 3 mm, = 100 ns, and f con =0.5, we find E = 6.2x10 3 I MA V/m, which is well below E BD. Faraday s law in integral form can be used to obtain the average inductive field. The result is. Since the electric field is very small within the conducting metal the field within the insulator is given by eq. 3 Equation 3 yields an electric field within the insulator of 9x10 5 V/m, assuming r L = 3 mm, f con =0.5, and B zi rises to 30 Tesla in 100 ns. The field within the insulator is comfortably below E BD. However, the electric field needed to breakdown an insulator at a surface can be significantly lower than the bulk breakdown field. This is further complicated by the presence of strong magnetic fields. Since it is difficult to numerically simulate this process, experiments have been planned to determine how large a magnetic field can be produced with this approach. Note that the electric field can be reduced by producing the magnetization field more slowly. The magnetization, breakdown and implosion phases of AutoMag are illustrated in Fig.4. Initially the drive current rises slowly during the magnetization phase we described in this section. The current rises 4

5 more quickly in the breakdown phase described in the next section. The current then rises to large values to drive the implosion phase. B. The breakdown phase At the end of the magnetization phase the drive current is designed to rise more quickly so the inductive electric field within the insulators is sufficient to cause breakdown. This is desired at this point for two reasons. First, we do not want the axial field within the fuel to become too large. Simulations indicate 4 that most of the implosion energy goes toward compressing the magnetic field (rather than the fuel) if the magnetic field is too large. The second reason is that once the fuel is magnetized we want both the metal and insulator materials to implode so that the fuel will be effectively compressed. Breakdown insures that the magnetic pressure will act on the both materials. Note that both the rate of current rise, di/dt, and f con can be used to control the time of breakdown. It is very difficult to numerically predict electrical breakdown accurately. The proper design will probably require experimental iteration. C. The implosion phase Once breakdown has occurred the drive current will flow primarily in the axial direction and the field driving the liner implosion will be. We want both the metal and the formerly insulating material to be accelerated at nearly the same rate. Since the azimuthal field driving the implosion will be nearly constant along the surface of the liner, this difference should be small if the insulator has the same density as the metal. The density of beryllium is 1.85 g/cc, while plastics and epoxies have densities of about 1.0 g/cc. Epoxies have been developed with a wide range of densities by adding relatively small quantities of other materials (dopants) with higher densities. An insulating dopant such as a metal oxide should be used, since the insulating properties must be preserved. We have performed 3D numerical simulations of an AutoMag liner implosion using the MHD code GORGON 15. Nylon with a density of 1.43 g/cc was used as the insulating material. This was a choice of convenience because equation-of-state tables were available. The initial geometry of the simulations is shown in Fig. 5. The dark blue represents the beryllium, while the nylon is shown in light blue. The 5

6 entire liner is helically wound with a pitch angle = 45 degrees. A view down the liner with the top electrode removed is shown in b) and c). Fig. 5c illustrates that field line tension tends to limit flute perturbations of the magnetic field. Dielectric breakdown is not explicitly handled in the calculation. As a finite volume code there is some numerical diffusion of mass into the first vacuum cell over time. This effectively low density material is able to start carrying a very small amount of current that slowly raises the temperature along that dielectric surface until it runs away and becomes more broadly conductive. The effect is that early in time most of the current flows in the metal, but eventually it switches to flowing along the entire surface. While the end result is that the calculation follows a reasonable transition between insulator and conductor, it s not modeling a physical breakdown process. Implementation of a more physical breakdown model is a priority for future work. The magnetic field generated when the drive current reaches 800 ka is plotted in Fig. 6: a) the azimuthally averaged field lines, and b) the axial field strength on axis. Equation 1 predicts a field strength of 32 Tesla which is in good agreement with the black curve which was obtained without the plastic spacers. The field is reduced when the plastic spacers are included due to the artificial breakdown process. 3D and 2D images of the liner are shown in Fig. 7 at three times during the implosion. The results show remarkable robustness to the large (30%) variation in density between nylon (light gray) and beryllium (purple for 3D rendering and dark gray for the midplane cuts). Note that the inside liner surface is essentially unperturbed even at the latest time, which is very encouraging. Calculations do indicate that maintaining a robust implosion does impose a minimum on the pitch angle that may be used for the helical windings, with perturbations seeded from these helical structures growing more aggressively as the pitch angle is reduced. Establishing the ideal pitch angle to generate sufficient field while maintaining a stable implosion would require more design work and likely some experimental iteration. It has been observed experimentally that liner implosions with an initial applied axial field exhibit helical perturbations which have a stabilizing effect on the implosions. Neither the cause of the helical perturbations nor the stabilizing effect are well understood, but suggests that the helical perturbation inherent in the AutoMag concept could be benign. Implosion experiments will be needed to confirm this. 6

7 III. AutoMag applications A. Low inductance feeds for high current MagLIF experiments 7-8 have been driven by current pulses that peak at MA. This is considerably lower than has been demonstrated (~25 MA) for other loads on Z such as the dynamic hohlraum 18. The main reason for this is the high initial inductance of the MagLIF power flow hardware (6.3 nh) which includes an extended MITL feed designed to axially center the MagLIF liner within the external field coils needed for magnetization, see Fig. 8a. Since AutoMag eliminates the need for exterior field coils a much lower inductance (3.7 nh) feed can be utilized as shown in Fig 8b. The operation of the Z machine from the Marx banks to the load can be modeled with the code Bertha 19. This model includes transmission lines, switches, electron losses in magnetically insulated transmission lines, plasma closure within transmission line gaps, ion losses in the convolute and final feed, resistive wall losses in conductors, and a model of the dynamic load impedance. Bertha accurately predicts the current for a large number of Z experiments without changing any of the model parameters. The Bertha predicted currents for the standard MagLIF feed and the low inductance AutoMag feed are plotted in Fig. 9. The peak current for AutoMag is 22 MA as compared to about 18 MA. Numerical simulations 14 predict the MagLIF yield scales strongly with peak current. Assuming optimal laser-preheat and no mixing of liner material into the fuel the simulations predict this current increase would increase the fusion yield by nearly a factor of ten. B. The generation and implosion of Field Reverse Configurations Field Reversed Configurations (FRCs) have been studied as a magnetic confinement configuration with the goal of fusion 20. An FRC is made with the following sequence of steps. First a tube is filled with low-density gas. A capacitor bank is used to drive current through coils around the tube to form an axial field within the tube and the gas. This field is typically referred to as the bias field. The gas is then ionized, usually by applying a high frequency component to the bias coils. The result is plasma with an imbedded axial magnetic field. Another capacitor bank then drives current into a separate set of coils, which apply an axial magnetic field to the plasma with the opposite polarity. This field both compresses and diffuses into the plasma. The oppositely directed magnetic fields undergo reconnection at each end 7

8 of the plasma and an FRC is formed. Numerical simulations 21 have successfully modeled the FRC formation process, but the effect of plasma instabilities producing anomalous resistivity was needed to predict the rate of reconnection The magnetic field and plasma density of an FRC with parameters relevant to an AutoMag experiment of the Z generator are depicted in Fig. 10a. This plot is the result of a GORGON simulation initiated with an approximate analytic solution and allowed to equilibrate over a 300 ns time interval. Note that less time would be needed if the initial solution were more accurate, but this result is just illustrative. We would need numerically simulate the formation process for an actual target design. Both the initial and final axial fields are plotted at the midplane in Fig. 10b. The equilibrated plasma and magnetic pressure at the midplane are plotted as a function of radius in Fig. 10c. Note that the total pressure (magnetic plus plasma) must be independent of the radius for equilibrium. The plasma pressure is equal to the maximum magnetic pressure at the radius where the magnetic field is zero. This is a significant advantage over most magnetically confined plasmas, which have pressures much less than the peak magnetic pressure. The early studies 20 showed that FRC lifetimes can be fairly long (~50 sec), but achieved ion temperatures of only about 1 kev, which is too low for significant fusion. It was proposed 22 that an FRC could be compressed by a liner implosion to increase the ion temperature and thus increase the fusion yield. Since the coils used to form the FRC would be in the way, it was also proposed translate the FRC from the region of formation to a region where the compression would occur. It was later demonstrated experimentally 23, that FRCs could be effectively translated. An experimental effort 24-26, was launched to generate, translate, and the compress an FRC using the Shiva Star pulsed power driver. It was concluded 26 that the FRCs produced in this experiment did not have a sufficient lifetime for effective compression. We present an alternative approach to the formation and compression of an FRC. The exterior coil system (ABZ) can be used to establish the bias field within an AutoMag liner containing deuterium or deuterium/tritium gas. Thin foils at each end can hold this gas in place. These foils can then be weakened with a low energy (several joules) laser pulse so that the gas pressure causes the foils to burst outward. A higher energy laser (several kj) then penetrates from one or both of the ends to heat the gas forming plasma in a manner essentially the same as standard MagLIF. The drive current passing through the AutoMag liner then generates an axial field with a polarity opposite to the bias field to create the 8

9 FRC. The AutoMag liner then breaks down to support axial current flow, and implodes onto the FRC to compress it and raise the ion temperature. If successful, this approach will produce FRCs with much higher magnetic fields and plasma densities than have been produced in the past. There will be no need to translate the FRCs, since they are formed in situ. Furthermore, the implosion time is only about 100 ns compared to about 20 sec for Shiva Star. This approach could provide an interesting alternative to the standard MagLIF approach. The gas density will be significantly lower for such an FRC than for MagLIF. The blast wave generated by the laser heating will be much less intense and should be confined by the magnetic field. This should lower any blast wave induced mix. Furthermore, the fusion plasma is not directly in contact with the liner walls. We have performed preliminary simulations and done analytic model calculations that both indicate interesting fusion yields should be possible from FRC implosions. The model calculations indicate that only modest gains (< 25) can be obtained for FRC implosions. It has been shown numerically 5 that MagLIF should be capable of attaining high gains ( ) by propagating the fusion burn to a dense layer of frozen deuterium/tritium on the inside of the liner. Perhaps this path to high gain is possible with FRC implosions. T IV. Discussion We have introduced a concept (AutoMag) to magnetize the fuel in a MagLIF implosion without the need of external field coils. AutoMag uses a composite liner with helical conduction paths separated by insulating material to generate the magnetization field from the early part of the drive current. The early part of the current is designed to rise slowly enough to avoid electrical breakdown of the insulation between the helical conductors long enough to generate the field needed to magnetize the fuel. Once fuel magnetization is established, the drive current rises more quickly and causes insulator break down. This allows the drive current to follow an axial path and implode the liner in the conventional z-pinch manner. There are two important advantages to AutoMag over external field coils for the operation of MagLIF. Low inductance magnetically insulated power feeds can be used to substantially increase the drive current and AutoMag does not interfere with diagnostic access even for 30 Tesla fields and larger. In comparison the present designs of external field coils capable of delivering 30 Tesla will completely 9

10 block diagnostic access. MagLIF could provide the high gains necessary for fusion energy, but external field coils, which are in close proximity to the fusion explosion, would be damaged each shot. This impracticality is removed by using AutoMag. Finally, AutoMag could make new magnetized high-energy-density experiments possible. An example is the generation of Field Reversed Configurations (FRC) by using both external field coils and AutoMag in opposite polarities. This would provide a means to study FRC formation with field strengths and plasma densities much larger than has been previously studied. Furthermore, FRC implosions could be studied on the 100 ns time scale, which should be much shorter than their natural lifetime. Acknowledgements We acknowledge useful discussions with R.D. McBride, D. C. Rovang, and M.R. Gomez. Sandia is a multi-program laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy s National Nuclear Security Administration under contract DE-AC04-94AL References 1 J. Lindl, Phys. Plasmas 2, 3933 (1995) 2 I. R. Lindemuth and R. C. Kirkpatrick, Nuclear Fusion 23, 263 (1983) 3 I. R. Lindemuth and M. M. Widner, Phys. Fluids 24, 746 (1981) 4 S. A. Slutz, M. C. Herrmann, R. A. Vesey, A. B. Sefkow, D. B. Sinars, D. C. Rovang, K. J. Peterson, M. E. Cuneo, Phys. Plasmas 17, (2010) 5 S.A. Slutz and R.A. Vesey, Phys. Rev. Lett. 108, (2012) 6 M. E. Cuneo, M. C. Herrmann, D. B. Sinars, S. A. Slutz. W.A. Stygar. R.A. Vesey, A.B. Sefkow, G.A. Rochau, G.A. Chandler, J.E. Bailey et al., IEEE Trans. Plasma Sci. 40, 3222 (2012). 7 M.R. Gomez, S.A. Slutz, A.B. Sefkow, D.B. Sinars, K.D. Hahn, S.B. Hansen, E.C. Harding, P.F. Knapp, P.F. Schmit, C.A. Jennings et al., Phys. Rev. Lett. 113, (2014). 8 M.R. Gomez, S.A. Slutz, A.B. Sefkow, K.D. Hahn, S.B. Hansen, P.F. Knapp, P.F. Schmit, C.L. Ruiz, D.B. Sinars, E.C. Harding et al., Phys. Plasmas 22, (2015) 9 C. L. Ruiz, G. W. Cooper, S. A. Slutz, J.E. Bailey, G.A. Chandler, T.J. Nash, T.A. Mehlhorn, R.J. Leeper, D. Fehl, A.J. Nelson et al., Phys. Rev. Lett. 93, (2004). 10 K. D. Hahn, G. W. Cooper, C. L. Ruiz, D.L. Fehl, G.A. Chandler, P.F. Knapp, R.J. Leeper, A.J. Nelson, R.M. Smelser, and J.A. Torres, Rev. Sci. Instrum. 85, (2014). 11 S.B. Hansen, M.R. Gomez, A.B. Sefkow, S.A. Slutz, D.B. Sinars, K.D. Hahn, E.C. Harding, P.F. Knapp, P.F. Schmit, T.J. Awe et al. Phys. Plasmas 22, (2015) 12 P. F. Schmit, P. F. Knapp, S. B. Hansen, M.R. Gomez, K.D. Hahn, D.B. Sinars, K.J. Peterson, S.A. Slutz, A.B. Sefkow, T.J. Awe et al., Phys. Rev. Lett. 113, (2014). 10

11 13 D.C. Rovang, D.C. Lamppa, M.E. Cuneo, A.C. Owen, J. McKenney, D.W. Johnson, S. Radovich, R.J. Kaye, R.D McBride, C.S. Alexander et al. Rev. Sci. Instrum. 85, (2014). 14 S.A. Slutz, W.A. Stygar, M.R. Gomez, K.J. Peterson, A.B. Sefkow, D.B. Sinars, R.A. Vesey, E.M. Campbell, and R. Betti, Phys. Plasmas, 23, (2016). 15 J. Chittenden, S.V. Lebedev, C.A. Jennings, S.N. Bland, and A. Ciardi, Plasma Phys. Controlled Fusion 46, B457 (2004) 16 T.J. Awe, R.D. McBride, C.A. Jennings, D.C. Lamppa, M.R. Martin, D.C. Rovang, S.A. Slutz, M.E. Cuneo, A.C. Owen, D.B. Sinars et al., Phys. Rev. Lett. 111, (2013) 17 T.J. Awe, K.J. Peterson, E.P. Yu, R.D. McBride, D.B. Sinars, M.R. Gomez, C.A. Jennings, M.R. Martin, S.E. Rosenthal, D.G. Schroen, A.B. Sefkow, S.A. Slutz, K. Tomlinson, and R.A. Vesey, Phys. Rev. Lett. 116, (2016) 18 G.A. Rochau, J.E. Bailey, R.E. Falcon, G.P. Losel, T. Nagayama, R.C. Mancini, I. Hall, D.E. Winget, M.H. Montgomery, and D.A. Liedahl, Phys. Plasmas 21, (2014). 19 D.D. Hinshelwood, Naval Research Laboratory Memorandum Report No. 5185, W.T. Armstrong, R.K. Linford, J. Lipson, D. A. Platts, and E.G. Sherwood, Phys. Fluids 24 (11), 2068, (1981). 21 R.D. Milroy, and J.U. Brackbill, Phys. Fluids 25 (5) 775 (1982). 22 R.L. Spencer, M. Tuszewski, and R.K. Linford, Phys. Fluids 26 (6) 1564 (1983) 23 D.J. Rej, W.T. Armstrong, R.E. Chrien, P.L. Klingner, R.K. Linford, K.F. McKenna, E.G. Sherwood, R.E. Siemon, and M. Tuszewski, and R.D. Milroy, Phys. Fluids 29 (3) 852 (1986) 24 T. P. Intrator, S.Y. Zhang, J.H. Degnan, I. Furno, C. Grabowski, S.C. Hsu, E.L. Ruden, P.G. Sanchez, J.M. Taccetti, M. Tuszewski et al., Phys. Plasmas (11) 2580 (2004) 25 T. P. Intrator, R.E. Siemon, and P.E. Sieck, Phys. Plasmas 15, (2008) 26 J.H. Degnan, D.J. Amdahl, M. Domonkos, F.M. Lehr, C. Grabowski, Nucl. Fusion 53, (2013) Figure Captions Fig. 1 (color) The geometry of MagLIF with external field coils Fig. 2 (color) MagLIF hardware on Z using split field coils a) and a single monolithic coil b) Fig. 3 (color) Schematic of the AutoMag geometry a), and illustration of contour for calculating the axial field inside (B zi ) and outside (B zo ) of the liner Fig. 4 (color) Three phases of AutoMag Fig. 5 (color) Initial geometry of 3D GORGON AutoMag simulation a) side view b) top view c) blow up of top view. The nylon insulator is shown in grey Fig. 6 (color) The magnetic field generated when the drive current reaches 800 ka a) the azimuthally averaged field lines, and b) the axial field strength on axis. Fig. 7 (color) 3D surface contours (left) and midplane cut (right) from GORGON simulations at times after the drive current reached 5 MA of a) 0.0 ns, b) 60 ns, and c) 80 ns. Fig. 8 (color) Power feeds for MagLIF with a) external coils and b) AutoMag Fig. 9 Simulated drive currents are plotted as a function of time. Fig. 10 (color) a) a contour plot of the magnetic field (black lines) and the plasma density, b) The axial field is plotted as a function of radius near the midplane, and c) The magnetic and plasma pressures are plotted as a function of radius at the midplane. 11

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