Influence of profile shape on the diocotron instability in a non-neutral plasma column
- Plasma Physics Laboratory, Princeton University, Princeton, New Jersey, 08543 (United States)
In this paper we examine theoretically the influence of density profile shape on the diocotron instability in a cylindrical, low-density ({omega}{sub pe}{sup 2}{lt}{omega}{sub ce}{sup 2}) non-neutral electron plasma column confined radially by a uniform axial magnetic field B{sub 0}{bold {cflx e}}{sub z}. The analysis assumes electrostatic flute perturbations ({partial_derivative}/{partial_derivative}z=0) about an axisymmetric equilibrium density profile n{sub e}{sup 0}(r), where r=(x{sup 2}+y{sup 2}){sup 1/2} is the radial distance from the column axis. Two classes of density profiles with inverted population in radius r are considered. These are the following: (a) a {ital step-function} density profile with uniform density {cflx n}{sub e}{center_dot}{Delta} in the column interior 0{le}r{lt}r{sub b}{sup {minus}}, and uniform density {cflx n}{sub e} in an outer annular region r{sub b}{sup {minus}}{lt}r{lt}r{sub b}{sup +}; and (b) a {ital continuously-varying} density profile of the form n{sub e}{sup 0}(r)={cflx n}{sub e}({Delta}+r{sup 2}/r{sub b}{sup 2})(1{minus}r{sup 2}/r{sub b}{sup 2}){sup 2} over the interval 0{le}r{lt}r{sub b}. Here, {cflx n}{sub e}, r{sub b}{sup {minus}}, r{sub b}{sup +} and r{sub b} are positive constants, and the dimensionless parameter {Delta} measures the degree of {open_quotes}hollowness{close_quotes} of the equilibrium density profile n{sub e}{sup 0}(r). Detailed linear stability properties are calculated for a wide range of system parameters, including values of the {open_quotes}filling factor{close_quotes} {Delta}, radial location r{sub w} of the cylindrical conducting wall, azimuthal mode number l, etc. As a general remark, in both cases, it is found that small increases in {Delta} from the value {Delta}=0 (corresponding to the strongest diocotron instability) can have a large effect on the growth rate and detailed properties of the instability. In addition, for the step-function density profile, the instability tends to be algebraic in nature and have a large growth rate in the unstable region of parameter space, whereas for the continuously-varying density profile, the instability is typically much weaker and involves a narrow class of resonant particles at radius r=r{sub s} satisfying the resonance condition {omega}{sub r}{minus}l{omega}{sub E}(r{sub s})=0. Here, {omega}{sub r}=Rethinsp{omega} is the real oscillation frequency, and {omega}{sub E}(r)={minus}cE{sub r}{sup 0}(r)/rB{sub 0} is the equilibrium {bold E}{sup 0}{times}B{sub 0}{bold {cflx e}}{sub z} rotation velocity of the plasma column. {copyright} {ital 1998 American Institute of Physics.}
- OSTI ID:
- 658481
- Journal Information:
- Physics of Plasmas, Journal Name: Physics of Plasmas Journal Issue: 10 Vol. 5; ISSN 1070-664X; ISSN PHPAEN
- Country of Publication:
- United States
- Language:
- English
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