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THE EFFECT OF SHEARED TOROIDAL FLOW ON AN FRC’S n=2 ROTATIONAL INSTABILITY Edward L. Ruden Air Force Research Laboratory, Directed Energy Directorate A Field Reversed Conguration (FRC) is observed to gain angular momentum until α = R /Di (rotational frequency over ion diamagnetic drift frequency) reaches a critical value, at which point an instability with azimuthal mode num- ber n = 2 dev elop s. Que stions remain as to whe ther the obs erved threshold is explai ned by publi shed calculati ons, which assume a rigid rotor pro le. Questions also remain as to the cause of the spin-up, but it necessarily involves angular momentum transpor t to the FRC thr ough the outer surf ace. Rotation of the bulk, then, via kinematic viscosity and/or convection can entail signicant veloc- ity shear. Rotation results in plasma (cen tripeta l) acceleratio n supported by an external magnetic eld, so the instability may be interpreted as a Rayleigh-Taylor (R-T) mode. Both sheared ow and Finite Larmour Radius (FLR) eff ects are recognized as mitigating factors for the R-T instability, and the two eff ects are synergistic. The rotational instability is investigated here using an analytic planar R-T model of an FLR plasma with a magnetically transverse sheared ow layer accel- erated by the magnetic eld. One result is that if the sheared layer is too thin to reach the magnetic (reve rsal) axis, it is unstable. The coupling between gyrovis- cosity and ow shear in this case negates the stabilizing e ff ect of both within a range of modes, and convection of the sheared layer to the magnetic axis can be expected to occur quickly. Once this happens, though, the FRC is stable until the shear factor reaches a high value, at which time the n = 2 mode goes unstable. Technically, n = 1 goes unstable rst, but the (planar) model applied to cylin- drical geometry does not conserve lateral linear momentum for this mode, so is inapplicable. This model provides insight into what may be an important feature of FRC stability, although less simplied calculati ons are needed. Nonet heless, it can be used tentatively to predict stability characteristics of an FRC during compres- sion by an electromagnetically imploded metal cylinder (for Magnetized Target Fusi on adi aba tic compr essi on) . Thi s is of conc ern sin ce acce ler ation from such an implosion supple ments centripetal acceleration, and α increases by a factor of 2.4, assuming angular momentum conservation, adiabatic compression, and the theoretical volume vs. radius scaling.

Edward L. Ruden- The Effect of Sheared Toroidal Flow on an FRC's n=2 Rotational Instability

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8/3/2019 Edward L. Ruden- The Effect of Sheared Toroidal Flow on an FRC's n=2 Rotational Instability

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8/3/2019 Edward L. Ruden- The Effect of Sheared Toroidal Flow on an FRC's n=2 Rotational Instability

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8/3/2019 Edward L. Ruden- The Effect of Sheared Toroidal Flow on an FRC's n=2 Rotational Instability

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8/3/2019 Edward L. Ruden- The Effect of Sheared Toroidal Flow on an FRC's n=2 Rotational Instability

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8/3/2019 Edward L. Ruden- The Effect of Sheared Toroidal Flow on an FRC's n=2 Rotational Instability

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8/3/2019 Edward L. Ruden- The Effect of Sheared Toroidal Flow on an FRC's n=2 Rotational Instability

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8/3/2019 Edward L. Ruden- The Effect of Sheared Toroidal Flow on an FRC's n=2 Rotational Instability

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