Waves in Non-Neutral Plasmas - Nonneutral Plasma Group

More documents

Recommendations

Info

December 21, 2012 6:0 World Scientific Review Volume - 9in x 6in anderegg˙waves˙nnps4 F. AndereggWe will describe later corrections to fdio ∞ to include the effect of a realisticplasma, that is, finite amplitude, finite length, temperature shift, etc.1.1.2. A negative energy modeThe diocotron mode is a negative energy mode. This can be easily seen inthe image charge model that we have used in this presentation. The imagecharge has the opposite sign of the “real” charge, therefore as the plasmais attracted towards its image charge, the electrostatic energy decreases asthe mode amplitude increases. Here any kinetic energy is ignored. Let’scalculate how much electrostatic energy is required to displace the plasmaby a distance D in the image charge electric field.W ES =∫ D0Q · E i dx =∫ D0( ) −NL qxN L qL p2πε 0 Rw2 dx= − (N Lq) 2 D 2L p < 0. (1.7)4πε 0R 2 wThe electrostatic energy W ES is negative; this means that the diocotronFig. 1.3. Sectored electrode with model of impedance Z. Growth rate plotted versusresistance R.mode can be destabilized by dissipation. This destabilization is referredto as “resistive growth.” Figure 1.3 illustrates how an azimuthal sectionof the wall (called a sector) can destabilize the dioctron mode. The powerdissipated in the load connected to the sector is P = 1 2 I2 Re(Z), where Iis the image current, and the electrostatic energy in the wave is W wave .
December 21, 2012 6:0 World Scientific Review Volume - 9in x 6in anderegg˙waves˙nnpsWaves in Non-neutral Plasma 5Therefore the growth rate of the wave is: 5γ =P= 4ε 0 ω 2 L 2 s sin 2 ∆θ2Re(Z) (1.8)2W wave π L pfor the RC circuit shown on Fig. 1.3 the real part of the impedance isRe(Z) =R1 + ω 2 R 2 C 2 . (1.9)This growth rate was carefully verified experimentally 5 as shown on Fig.1.3. As the external resistance R is increased, the growth rate increaseslinearly up to a maximum corresponding to ω 2 R 2 C 2 = 1; at the maximumgrowth rate, half of the current is flowing through the resistor and theother half through the capacitor. As R is further increased, the growth rateis reduced since more and more current flows through the dissipationlesscapacitor. Figure 1.3 also shows the growth rate for a different capacitor,further validating the model. Figure 1.4 shows how a feedback circuit canFig. 1.4.shift.Schematic of diocotron feedback circuit and feedback growth rate versus phasebe used to damp a diocotron mode, by phase-shifting the sector voltage soas to obtain an effective “negative resistance.” Changing the phase of thefeedback controls the growth or damping rate of the diocotron mode. 6The diocotron mode provides a useful technique to control the positionof the plasma in a trap. For example Fig. 1.5 shows a “phaser” pictures ofz-integrated density obtained by multiple dumps and measuring the chargepassing through a collimator hole at varying azimuthal positions of theplasma. 7 Also the diocotron mode is a good tool to load off axis multitrapcells 8 designed to store large numbers of particles such as positrons.
Page 1: December 21, 2012 6:0 World Scienti
Page 6 and 7: December 21, 2012 6:0 World Scienti
Page 20: December 21, 2012 6:0 World Scienti

Waves in Non-Neutral Plasmas - Nonneutral Plasma Group

Create successful ePaper yourself

Delete template?

Save as template?