G.H." Miley

H. "Momota

Y. Tomita

National Institute for Fusion Science (NIFS-Repository)

§20. Analytical Studies on a Traveling Wave Di-rect Energy Converter for D-3He Fusion Momota, H., Tomita, Y. Miley, G.H. (Univ. of Illinois) Analytical studies on a traveling wave direct energy converter (TWDEC) [ 1 ,2] for D-3He fueled fusion are carried out. The TWDEC consists of a modulator and a decelerator both of which consist of an array of metallic grid meshes and a transmission circuit. The applied traveling wave potential to the modulator modulates the velocity of fusion proton beams. This modulation makes a form of bunched protons at a down stream of the modulator: 4neVmo . np(x,t) = npo[ 1 + 2 stn(kmx- mmt)], (1) mv1 here, V mo, k m and Wm are the potential, ·wave-number and frequency of the applied wave, respectively, and v t corresponds a Doppler spread at the birth of fusion protons. The second term indicates the spatial bunching at the down stream of the modulator field. At the decelerator, the wave number kd of the potential wave ye.due to bunched protons is changed spatially by the coupling to the excited traveling wave on the transmission circuit (Fig .1). From this circuit the potential V n is governed by a forced oscillation due to the potential of bunched protons: (2 C s) ( .. R . ) V n [ .. .. +C Vn+ L Vn + LC- Vn+1+Vn-1+ R ( . . )] C s ( · · e R · e) (2) L Vn+1+Vn-1 = -zvn+LVn · In this transmission circuit, the form of the potential wave can be transmitted is given by: V nU) = f p(t) COS (On- Wdt) , (3) here 8 n is the phase of n-th grid and the function f changes much slower than the traveling wave. Onder this situation we have a non-trivial solution, provided that the resonance condition: 2 v2 g2 - md - 4 = 0 , (4) is satisfied. Here 0 is the characteristic frequency of the transmission circuit: 286 g2= 1 - LC[2(1-y)+CsiC]' and v = RIL. The potential V0 of n-th grid is obtained: Vn(t) = [ Vn(O) exp(-vtl 2) COS \fn(O) (5) e v2 --(1 + )-1 I 2(1- exp( -vt I 2))] vmd 16md 2 X COS\{' n (t), (6) here, ~ 2 Cs - V 1 e=md -V 1+--------, C md 2 2(1-y)+CsiC Xn 4md \fn(t) = J kdd~- mdt -l/J + tan-1-, v 1 l/J =- cos-1 I , y = cos(On+1- On). ""V1 + R2 I L 2 As a result the power obtained from the decelerator is given by using the steepness of resonance Q ( = WdLI R) Pout = 8e2 Q5 m~L (16Q2 + 1) (Q2 + 1) · (7) ' I I I grid meshes I I I Fig.1 The transmission circuit in the decelerator, consists of a inductance L, a capacitor C, and a register R. The stray capacitance between proton beams and grid meshes is denoted by C8 • Reference 1) Momota, H., LA-11808-C, Los Alamos Natl. Lab., New Mexico, (1989) 8. 2) Shu, L.Y, Miley, G.H., Tomita, Y, and Momota, H., Trans. Fusion Technol., 27 (1995) 551. 

Analytical Studies on a Traveling Wave Direct Energy Converter for D-3He Fusion

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