Matthew Weis

Effects of magnetic shear on magneto-Rayleigh-Taylor instability

The magnetized liner inertial fusion concept [S. A. Slutz et al., Phys. Plasmas 17, 056303 (2010)] consists of a cylindrical metal liner enclosing a preheated plasma that is embedded in an axial magnetic field. Because of its diffusion into the liner, the pulsed azimuthal magnetic field may exhibit a strong magnetic shear within the liner, offering the interesting possibility of shear stabilization of the magneto-Rayleigh-Taylor (MRT) instability. Here, we use the ideal MHD model to study this effect of magnetic shear in a finite slab. It is found that magnetic shear reduces the MRT growth rate in general. The feedthrough factor is virtually independent of magnetic shear. In the limit of infinite magnetic shear, all MRT modes are stable if bu > 1, where bu is the ratio of the perturbed magnetic tension in the liner’s interior region to the acceleration during implosion.

Magneto-Rayleigh-Taylor experiments on a MegaAmpere linear transformer driver

Experiments have been performed on a nominal 100 ns rise time, MegaAmpere (MA)-class linear transformer driver to explore the magneto-Rayleigh-Taylor (MRT) instability in planar geometry. Plasma loads consisted of ablated 400 nm-thick, 1 cm-wide aluminum foils located between two parallel-plate return-current electrodes. Plasma acceleration was adjusted by offsetting the position of the foil (cathode) between the anode plates. Diagnostics included double-pulse, sub-ns laser shadowgraphy, and machine current B-dot loops. Experimental growth rates for MRT on both sides of the ablated aluminum plasma slab were comparable for centered-foils. The MRT growth rate was fastest (98 ns e-folding time) for the foil-offset case where there was a larger magnetic field to accelerate the plasma. Other cases showed slower growth rates with e-folding times of about ∼106 ns. An interpretation of the experimental data in terms of an analytic MRT model is attempted.

Coupling of sausage, kink, and magneto-Rayleigh-Taylor instabilities in a cylindrical liner

This paper analyzes the coupling of magneto-Rayleigh-Taylor (MRT), sausage, and kink modes in an imploding cylindrical liner, using ideal MHD. A uniform axial magnetic field of arbitrary value is included in each region: liner, its interior, and its exterior. The dispersion relation is solved exactly, for arbitrary radial acceleration (-g), axial wavenumber (k), azimuthal mode number (m), liner aspect ratio, and equilibrium quantities in each region. For small k, a positive g (inward radial acceleration in the lab frame) tends to stabilize the sausage mode, but destabilize the kink mode. For large k, a positive g destabilizes both the kink and sausage mode. Using the 1D-HYDRA simulation results for an equilibrium model that includes a pre-existing axial magnetic field and a preheated fuel, we identify several stages of MRT-sausage-kink mode evolution. We find that the m = 1 kink-MRT mode has a higher growth rate at the initial stage and stagnation stage of the implosion, and that the m = 0 sausage-MRT mod...

Temporal evolution of surface ripples on a finite plasma slab subject to the magneto-Rayleigh-Taylor instability

Using the ideal magnetohydrodynamic model, we calculate the temporal evolution of initial ripples on the boundaries of a planar plasma slab that is subjected to the magneto-Rayleigh-Taylor instability. The plasma slab consists of three regions. We assume that in each region the plasma density is constant with an arbitrary value and the magnetic field is also constant with an arbitrary magnitude and an arbitrary direction parallel to the interfaces. Thus, the instability may be driven by a combination of magnetic pressure and kinetic pressure. The general dispersion relation is derived, together with the feedthrough factor between the two interfaces. The temporal evolution is constructed from the superposition of the eigenmodes. Previously established results are recovered in the various limits. Numerical examples are given on the temporal evolution of ripples on the interfaces of the finite plasma slab.

Experimental investigation of the effects of an axial magnetic field on the magneto Rayleigh-Taylor instability in ablating planar foil plasmas

Summary form only given. Experiments are underway to study the effects an axial magnetic field on the magneto Rayleigh-Taylor instability (MRT) in ablating planar foils on the 1-MA LTD at the Michigan Accelerator for Inductive Z-pinch Experiments (MAIZE) facility at the University of Michigan. In planar foil ablation experiments at UM, MRT is observed when the expanding plasma-vacuum interface decelerates as the magnetic pressure exceeds the plasma pressure during the drive current1. Theoretical investigation at UM has shown that an axial magnetic field along with magnetic shear may reduce the MRT growth rate in general2. To test this experimentally, axial magnetic fields are generated using helical return current posts. The axial field is proportional to the drive current and peaks at 13 T for 600 kA peak current. A 775 nm Ti:sapphire laser is used to shadowgraph the foil in order to study the MRT instability. Results indicate improved confinement in addition to significant anisotropy on the left and right sides of the foil when compared to experiments at UM using planar return current posts with no axial field. Recent work utilizes a new load configuration where return current plates run perpendicular to the foil current, producing an axial field that can be adjusted based on the proximity of the plates to the foil.

Effects of axial magnetic field on mhd instabilities in cylindrical liners

Summary form only given. This paper analyzes the effects of an axial magnetic field on the magneto-Rayleigh-Taylor instability (MRT) of an imploding cylindrical liner. In recent MagLIF experiments with a premagnetized axial magnetic field [1], helical perturbations on the outer surface of the liner were found to persist despite the severe winding up of the magnetic field streamline. The inner surface of the liner exhibited improved integrity as a result of the premagnetized axial magnetic field. Here, we propose that the helical structure is the signature of the azimuthal m = 1 eigenmode with axial wavenumber k, so that the pitch angle of the helix, phi = arctan(m/kr) ~ 1/kr. Here, r is the outer radius of the imploding liner at which the helical perturbations were observed [1]. This simple scaling shows that phi increases as the convergence ratio (CR) increases, i.e., as r decreases. It also qualitatively explains the evolution of phi in both the low CR and high CR shot data that were tabulated in [1]. We have extended our MRT theory for the slab geometry [2] to a cylindrical geometry, so as to include the coupling between MRT, the sausage mode (m = 0) and the kink mode (m = 1). The effect of feedthrough suppression by the strong axial magnetic field is noted. Instantaneous equilibrium profiles obtained from 1-D HYDRA runs have been applied to the aforementioned formulation.

Feedthrough of the Magneto-Rayleigh-Taylor instability in the presence of a shock

Summary form only given. The success of the Magnetized Liner Inertial Fusion (MagLIF) campaign requires successful mitigation of the Magneto-Rayleigh-Taylor instability (MRT). Initially, the exterior of the liner is MRT unstable; as the accelerated liner compresses a fill gas, it is eventually decelerated by the back pressure of the fill gas causing the inner surface to become MRT unstable. It is thought that feedthrough of MRT from the outer to inner surface can provide a seed for disruptive growth in the deceleration phase. A common method of studying MRT is by machining sinusoidal ripples on the exterior of metal targets (Al, Be in particular). This seeding provides a known wavelength for MRT whose growth can then be compared with linear theory. For the exterior of Al liners, linear MRT theory works quite well [1] and thus, feedthrough theory should apply equally well to the inner surface for an unshocked seeded liner. However, in most shots on the Z-machine a shock is driven through the liner. 2D HYDRA simulations show the shock is rippled with the seeded wavelength and imprints this ripple on the inner surface as it breaks-out. The amplitude of this ripple could be much larger than what would be expected from the feedthrough of MRT theory [2]. Thus, to study feedthrough directly either isentropic compression is required, or we must include the effect of the shock on feedthrough. We propose a simple model to determine the imprinted ripple amplitude from a shock and then calculate the evolution of the inner surface ripple using traditional MRT [2] and Richtmyer-Meshkov theory and then compare to 2D HYDRA results. This model allows for simultaneous study of outer/inner surface growth from an exterior seeded perturbation and includes the effect of feedthrough. We also examine the impact of axial magnetic fields and fill gases (cool and pre-heated) on feedthrough and shock imprinting by applying our model and compare with 2D simulations.

A property of the Rayleigh-Taylor instability

Summary form only given. In his classic paper, Taylor [1] considered the instability on the surfaces of a fluid slab of a finite thickness that is accelerated by a much lighter fluid on either side of the fluid slab. The maximum number of e-foldings in the amplitude growth of the Taylor instability of this fluid slab is given by sqrt(2ks), where k is the wavenumber of the interface perturbation, and s is the distance traveled by the accelerated fluid slab, according to the linear theory. We show that this bound is independent of the magnitude and sign of the acceleration, of the magnitude and sign of the initial velocity of the slab, and of the width of the fluid slab. The primary dependence on the accelerated distance is illustrated in the resistive MHD radiation-hydrodynamics code, HYDRA [2], in which an aluminum slab with an initial sinusoidal surface ripple is accelerated by an intense magnetic pressure. Despite the nine times increase in magnetic pressure (from B = 200 T to 600 T), there is little difference in the Rayleigh-Taylor instability growth after the slab is accelerated for the same distance. This insensitivity to B appears to be the case in the simulation with or without the stabilization effect of the magnetic tension.

Spectroscopic analysis of foil plasmas on a 1-MA Linear Transformer Driver

Spectroscopic analysis has been performed on Al foil plasmas ablated by the Linear Transformer Driver (LTD) at the University of Michigan. The MAIZE LTD can supply 1-MA, 100 kV pulses with 100 ns risetime into a matched load. The plasma load used in this experiment consists of a 400 nm Al foil (cathode) placed between two, planar, current return anode posts. The LTD was charged to +−70 kV, resulting in approximately 0.65 MA with a 170 ns risetime passing through the foil. An optical fiber was placed about 1 cm away from the load; plasma light passed through a 0.75-m optical spectrograph and was gated for 10 ns by an intensified CCD detector.

Experiments on MA linear transformer drivers

Linear Transformer Drivers (LTDs) represent the most compact, high-current accelerators. LTDs have numerous advantages over Marx PFL systems: a) fast risetime (100 ns) without additional pulse forming, b) high efficiency (∼70%), c) inductive voltage adder and d) repetitively pulsed operation. LTDs have been utilized in a patented Sandia design for a PW pulsed power driver for fusion.[1] MYKONOS, a 1-MV, 1-MA LTD system is being constructed at Sandia. The 1-MA, 100 kV LTD at UM was designed and developed at the IHCE under Sandia sponsorship. Initial tests were performed at IHCE in an inductive-adder with 5 LTD modules at 1-MA and 0.5 MV. At UM, the LTD was coupled to a Magnetically Insulated Transmission Line (MITL) to drive a load in the MAIZE z-pinch facility. Resistive load tests agreed well with PSPICE simulations. Modifications have been made to the UM LTD to improve its serviceability in an experimental system. Magneto-Rayleigh-Taylor plasma instability experiments have been performed on the UM LTD facility in a low-inductance, planar-foil plasma load, located between two planar anode plates.[2] Laser shadowgraphy was performed by a 100-sps doubled-YAG laser. Instability growth rate have been compared to MRT theory (Lau et al., this conference). PSPICE simulations of LTD component voltages and currents have been performed, accounting for calculated foil motion. UM LTD convolute experiments were performed.[3]