Fundamentals of Plasma Physics

482 Chapter 16. Non-neutral plasmas

perfectly

conducting

w all

perfectly

conducting

wall

(a) (b)

(c)

(d)

pure

electron

plasma

pure

electron

plasma

pure

electron

plasma

segment segment

R

R

C L

anode

cathode

inductance

capacitance

electron cloud

Figure 16.6: (a) Pure electron plasma with one wall segment connected to ground via a
resistorR,(b) same, but now connected to ground via a resonant circuit consisting of
a capacitorCin parallel with a coilLand a resistorR,(c) same, but now a set of 10
resonant circuits connected across 10 gaps, (d) same, but now the coil is a single turn and
the capacitance is in the leads connecting to the coil (the resistor is the loading of the
coupler to the output circuit, typically a loop inserted into a coil).

7. Spiral due to sheared rotation:Suppose that a non-neutral plasma has a sheared angu-
   lar velocity so thatω 0 =ω 0 (r).Suppose that a radial line is painted onto the plasma
   att=0extending fromx=rp/ 4 ,y=0tox=rp/ 2 ,y=0whererpis the plasma
   radius. Suppose thatω 0 = ̄ω 0 r/rp. Calculate the trajectory of points on the painted
   line and plot this for successive times using a computer. If the initial linehad finite
   thickness and hence finite area, what would happen to the thickness of the linewith
   increasing time?