Stability Of Plasma Configurations During Compression

Magnetized Target Fusion (MTF) efforts are based on calculations showing that the addition of a closed magnetic field reduces the driver pressure and rise time requirements for inertial confinement fusion by reducing thermal conductivity. Instabilities that result in convective bulk transport at the Alphen time scale are of particular concern since they are much faster than the implosion time. Such instabilities may occur during compression due to, for example, an increase in the plasma-magnetic pressure ratio {beta} or, in the case of a rotating plasma, spin-up due to angular momentum conservation. Details depend on the magnetic field topology and compression geometry. A hard core z pinch with purely azimuthal magnetic field can theoretically be made that relaxes into a wall supported diffuse profile satisfying the Kadomtsev criterion for the stability of m = 0 modes, which is theoretically preserved during cylindrical outer wall compression. The center conductor radius and current must also be large enough to keep the {beta} below stability limits to stabilize modes with m > 0. The stability of m > 0 modes actually improves during compression. A disadvantage of this geometry, though, is plasma contact with the solid boundaries. In addition to the risk of high Z impurity contamination during the (turbulent) relaxation process, contact thereafter can cause plasma pressure near the outer surface to drop, violating the Kadomtsev criterion locally. The resultant m = 0 instability can then convect impurities inward. Also, the center conductor (which is not part of the Kadomtsev profile) can go m = 0 unstable, convecting impurities outward. One way to mitigate impurity convection is to instead use a Woltjer-Taylor minimum magnetic energy configuration (spheromak). The sheared magnetic field inhibits convection, and the need for the center conductor is eliminated. The plasma, however, would likely still have to be wall supported due to unfavorable {beta} scaling during quasispherical (3-D) compression otherwise. Use of a Field Reversed Configuration (FRC) substantially resolves the wall contact issue, but at the cost of introducing a new (rotational) instability. An FRC has an open magnetic field outside a separatrix which effectively diverts wall material. However, FRC particles diffusing across the separatrix have a preferred angular momentum, causing the FRC within to counter-rotate in response. When the FRC's rotational-diamagnetic drift frequency ratio {alpha} reaches a critical value of order unity, the FRC undergoes a rotational instability that results in rapid particle loss. The instability is exacerbated by cylindrical compression since {beta} {approx} R{sup -2/5} during this phase, assuming angular momentum conservation. A multipole magnetic field frozen into the solid liner during compression may stabilize this mode directly and/or by impeding spin-up without significantly perturbing the implosion's azimuthal symmetry