Nonlinear saturation of the parallel velocity shear instability
- Massachusetts Institute of Technology, Cambridge, MA (United States)
Plasma flows in the direction parallel to the ambient magnetic field are nearly ubiquitous. They occur naturally in linear plasma columns or in toroidal experiments under a variety of conditions. These flows are also observed in the near-Earth environment as the solar wind is deflected by the bow shock and flows past the flanks of the magnetosphere. A shear in the flow (i.e., B x {del}V{sub {parallel}} {ne} 0) can lead to instabilities and spontaneous break-up of the flow. In driven systems, saturation by quasilinear processes such as relaxation of the velocity gradient is not realistic, thus one is led to consider other processes such as the coupling to a damped mode. Linear stability analysis predicts two very distinct limits for the velocity shear problem. With relatively large values of the velocity gradient (dV{sub {parallel}}/dx {approximately} V{sub thi}/ L{sub n}) a mode first found by D`Angelo can occur. This mode is characterized by ({gamma} >> {omega}{sub r}) but is easily stabilized in the presence of significant density gradients. A new dissipative instability can occur for relatively low values of the velocity gradient as first suggested by Coppi. The relevant dissipation can enter through a parallel ion viscosity or ion-neutral collisions. This mode is characterized by ({omega}{sub r} {approx} {omega}{sub *e} >> {gamma}) and is not stabilized by the presence of density gradients. In our nonlinear analysis, we consider both the strongly growing D`Angelo mode and Coppi`s weakly growing dissipative mode. A plane geometry including both density and velocity gradients is analyzed with two fluid equations. The linear stability of these modes is such that if a mode with wave number k is unstable then so are all of its harmonics (2k, 3k, ... ). The inclusion of FLR corrections in the fluid equations introduces a stability boundary in k-space so that we may consider a single linearly unstable eigenmode coupled to a linearly damped harmonic.
- OSTI ID:
- 489427
- Report Number(s):
- CONF-960354-; TRN: 97:011571
- Resource Relation:
- Conference: International Sherwood fusion theory conference, Philadelphia, PA (United States), 18-20 Mar 1996; Other Information: PBD: 1996; Related Information: Is Part Of 1996 international Sherwood fusion theory conference; PB: 244 p.
- Country of Publication:
- United States
- Language:
- English
Similar Records
Stability theory of dissipative trapped-electron and trapped-ion modes
New parallel velocity shear instability