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Improved feedback stabilization of interior plasma modes
Volume 60A, number 2
PHYSICS LETTERS
7 February 1977
IMPROVED FEEDBACK STABILIZATION OF INTERIOR PLASMA MODES R. JONES Stevens Institute of Technology, Hobo ken, New Jersey 07030, USA
1
Received 6 October 1976 Revised mai~uscriptreceived 11 January 1977 RF loaded particulate beams can efficiently penetrate a plasma and stabilize internal localized modes.
One of the principal difficulties with feedback stabilization is the efficient coupling of the response signal back into the appropriate region of the plasma. While surface waves have been effectively stabilized by this technique [1] its usefulness for interior modes suffers from the same problems as RF heating experiments. That is, one finds, for some of the RF methods envisaged, a saturation of the energy transfer process [2] and a strong dependence of the coupling efficiency upon the time variable boundaries [3]. We have recently suggested that energy be coupled into plasmas by imposing strong RF signals on injected particle beams [4] (through the use of slow wave structures). Not only is this practical with ion or electron beams but it is even possible with neutral beam injectors by coupling in the RF energy prior to the charge exchange cell. There is no reason why the modulation power can not exceed the beam kinetic energy should ion source efficiency be low at the velocity desired for effective penetration of the plasma. In the present experiment we use such “bunched beams” of “beams antennas” to apply stabilizing signals to internal electrostatic plasma modes. Walsh has previously shown [1] that feedback stabilization is effective in suppression of the instability of a fast, cold electron beam passing through a plasma. For this instability the beam carrying the “stabilizing response” is also the energy source that drives the plasma modes into instability. This will do nothing to weaken our line of argumerItation, however, since the question is simply one of energy coupling efficiency. Furthermore, we will see that feedback induced detuning of the beam-plasma instability (to either reduce 1
Present address: General Atomic Co., San Diego, California, USA.
or enhance it) is of practical interest for certain CTR studies. In the experiment of Walsh [1] the feedback response signal was applied with electrostatic loops just inside the plasma column. The coupling constant measured for this system was subsequently reported [5] as —27 dB and said to be in reasonable agreement with antenna theory. The present beam-plasma experiment resembles our earlier work [61 except that RF modulation can be applied directly to the beam distribution at the diode. We compare this mode of operation with that possible with 3.4 cm diameter loop antennasjust inside the 4cm diameterplasma column. The experiment is performed in the H wave regine (i.e. ~~p> ~ and the mode designation convention of reference [6] with a 5 mm diameter electron beam. We have previously shown that the unstable linear waves are confined to the beam region [6], i.e. interior modes (localized). A confining field of 200 gauss was present and the observed plasma density and temperature were n~, 5 X i09 cm3 and 5 eV respectively. The initial beam energy is 400 volts with spread of 20 volts (initial half width). An electrostatic energy analyzer terminates the system 25 cm from the diode and analyzes the stability of the transmitted beam distribution. Its resolution is about 1% at these energies. (See our ref. [6] for further details of the experimental geometry, etc.) By using the analyzer as reference a fixed amplitude signal source was applied to the antenna loop or beam diode and tuned in frequency until maximum stabilization was observed. In both cases this occurs at about 720 MHz. Additionally, the loop antenna was positioned axially for optimal response. This occurs at about 5 cm from the diode. 117
Volume 60A, number 2
PHYSICS LETTERS
as an example but does, in itself, represent a problem of some practical interest. If one wants to heat long linear fusion reactors, for instance, it is necessary to spread the heating out over a long plasma region. While lasers offer one possibility electron beams are an efficient and available alternative if the relaxation
teJ\~ 0
o o
7 February 1977
310
900
length canused be controled [7].enhance The present technique could be to reduce or the natural heating profile. A passive, autoresonant wave structure could be used to modulate the e beam produced from a conventional relativistic diode source. The prescription for detuning the unstable waves is discussed in ref. [1].
E(eV) Fig. 1. Stability of the transmitted beam distribution as a function of feedback. (A) With RF loaded on beam; (B) with RF launched in plasma; (C) RF off. flb/flp 0.01.
In fig. I we show the relative stabilization obtained. Curve A shows the best stability observed. It is achieved by application of the RF on the injected beam at the diode. The transmitted beam is only very slightly different from the original injected beam. Curve B shows the result of the same signal applied to the ioop antenna and tuned for best response. The beam is rather badly spread in energy, though some stabilization is noted as compared with curve C, the result without feedback stabilization. The coupling efficiencies are poorly known. Estimates are that the antenna coupling efficiency is —15 to —10 dB while the diode electrode coupling is probably better than —5 dB. The present experiment is intended principally
118
This work was begun at Stevens Institute under finding from the National Sceince Foundation and completed in the author’s laboratory privately.
References [1] T.K. Chu and H.W. Hendel (eds.), Feedback and dynamic control of plasmas, Amer. Inst. of Phys., New York,, 1970). 121 H. Toyana, and K. Matsura, Nucl. Fusion 13 (1973) 363. [3J A. Messiaen, P. Vandenplas, R. Weynants and R. Koch, Nuci. Fusion 15 (1975) 75. [4] R. Jones, Phys. Lett., to be published. [5] J.R. Conrad, C.J. Diaz, and J.E. Walsh, Phys. Fluids 16 (1973) 1300. [6] M. 19 Seidi, (1976)W.78.Carr, D. Boyd, and R. Jones, Phys. Fluids [7] E.g., J. Benford, Electron beam heating of linear fusion devices, presented at the First Intern. Conf. on Electron beam research and technology, Albuquerque, November 3—5~1975.
PHYSICS LETTERS
7 February 1977
IMPROVED FEEDBACK STABILIZATION OF INTERIOR PLASMA MODES R. JONES Stevens Institute of Technology, Hobo ken, New Jersey 07030, USA
1
Received 6 October 1976 Revised mai~uscriptreceived 11 January 1977 RF loaded particulate beams can efficiently penetrate a plasma and stabilize internal localized modes.
One of the principal difficulties with feedback stabilization is the efficient coupling of the response signal back into the appropriate region of the plasma. While surface waves have been effectively stabilized by this technique [1] its usefulness for interior modes suffers from the same problems as RF heating experiments. That is, one finds, for some of the RF methods envisaged, a saturation of the energy transfer process [2] and a strong dependence of the coupling efficiency upon the time variable boundaries [3]. We have recently suggested that energy be coupled into plasmas by imposing strong RF signals on injected particle beams [4] (through the use of slow wave structures). Not only is this practical with ion or electron beams but it is even possible with neutral beam injectors by coupling in the RF energy prior to the charge exchange cell. There is no reason why the modulation power can not exceed the beam kinetic energy should ion source efficiency be low at the velocity desired for effective penetration of the plasma. In the present experiment we use such “bunched beams” of “beams antennas” to apply stabilizing signals to internal electrostatic plasma modes. Walsh has previously shown [1] that feedback stabilization is effective in suppression of the instability of a fast, cold electron beam passing through a plasma. For this instability the beam carrying the “stabilizing response” is also the energy source that drives the plasma modes into instability. This will do nothing to weaken our line of argumerItation, however, since the question is simply one of energy coupling efficiency. Furthermore, we will see that feedback induced detuning of the beam-plasma instability (to either reduce 1
Present address: General Atomic Co., San Diego, California, USA.
or enhance it) is of practical interest for certain CTR studies. In the experiment of Walsh [1] the feedback response signal was applied with electrostatic loops just inside the plasma column. The coupling constant measured for this system was subsequently reported [5] as —27 dB and said to be in reasonable agreement with antenna theory. The present beam-plasma experiment resembles our earlier work [61 except that RF modulation can be applied directly to the beam distribution at the diode. We compare this mode of operation with that possible with 3.4 cm diameter loop antennasjust inside the 4cm diameterplasma column. The experiment is performed in the H wave regine (i.e. ~~p> ~ and the mode designation convention of reference [6] with a 5 mm diameter electron beam. We have previously shown that the unstable linear waves are confined to the beam region [6], i.e. interior modes (localized). A confining field of 200 gauss was present and the observed plasma density and temperature were n~, 5 X i09 cm3 and 5 eV respectively. The initial beam energy is 400 volts with spread of 20 volts (initial half width). An electrostatic energy analyzer terminates the system 25 cm from the diode and analyzes the stability of the transmitted beam distribution. Its resolution is about 1% at these energies. (See our ref. [6] for further details of the experimental geometry, etc.) By using the analyzer as reference a fixed amplitude signal source was applied to the antenna loop or beam diode and tuned in frequency until maximum stabilization was observed. In both cases this occurs at about 720 MHz. Additionally, the loop antenna was positioned axially for optimal response. This occurs at about 5 cm from the diode. 117
Volume 60A, number 2
PHYSICS LETTERS
as an example but does, in itself, represent a problem of some practical interest. If one wants to heat long linear fusion reactors, for instance, it is necessary to spread the heating out over a long plasma region. While lasers offer one possibility electron beams are an efficient and available alternative if the relaxation
teJ\~ 0
o o
7 February 1977
310
900
length canused be controled [7].enhance The present technique could be to reduce or the natural heating profile. A passive, autoresonant wave structure could be used to modulate the e beam produced from a conventional relativistic diode source. The prescription for detuning the unstable waves is discussed in ref. [1].
E(eV) Fig. 1. Stability of the transmitted beam distribution as a function of feedback. (A) With RF loaded on beam; (B) with RF launched in plasma; (C) RF off. flb/flp 0.01.
In fig. I we show the relative stabilization obtained. Curve A shows the best stability observed. It is achieved by application of the RF on the injected beam at the diode. The transmitted beam is only very slightly different from the original injected beam. Curve B shows the result of the same signal applied to the ioop antenna and tuned for best response. The beam is rather badly spread in energy, though some stabilization is noted as compared with curve C, the result without feedback stabilization. The coupling efficiencies are poorly known. Estimates are that the antenna coupling efficiency is —15 to —10 dB while the diode electrode coupling is probably better than —5 dB. The present experiment is intended principally
118
This work was begun at Stevens Institute under finding from the National Sceince Foundation and completed in the author’s laboratory privately.
References [1] T.K. Chu and H.W. Hendel (eds.), Feedback and dynamic control of plasmas, Amer. Inst. of Phys., New York,, 1970). 121 H. Toyana, and K. Matsura, Nucl. Fusion 13 (1973) 363. [3J A. Messiaen, P. Vandenplas, R. Weynants and R. Koch, Nuci. Fusion 15 (1975) 75. [4] R. Jones, Phys. Lett., to be published. [5] J.R. Conrad, C.J. Diaz, and J.E. Walsh, Phys. Fluids 16 (1973) 1300. [6] M. 19 Seidi, (1976)W.78.Carr, D. Boyd, and R. Jones, Phys. Fluids [7] E.g., J. Benford, Electron beam heating of linear fusion devices, presented at the First Intern. Conf. on Electron beam research and technology, Albuquerque, November 3—5~1975.