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Energy loss effects on turbulent heating
PHYSICS LETTERS
Volume 42A, number 5
1 January 1973
ENERGY LOSS EFFECTS ON TURBULENT HEATING* K.A. GERBER and G.C. GOLDENBAUM Naval Research Laboratory, Washington, D.C. 20390, USA Received 14 November 1972
Experimental evidence is presented for the effect of electron energy loss on determining the type of cross field electron streaming instability that develops in low density, high temperature plasmas.
Plasma instabilities involving electrons streaming with respect to ions across magnetic field lines have received a great deal of attention in the last few years. The interpretation of some experimental investigations of plasma heating based on these instabilities has been complicated because of the possibility of electron energy loss along the magnetic field lines [ 1,2] . The experiments we refer to involve low density theta pinches. It has been found that when the theta pinch is operated without an initial bias magnetic field or ‘with a bias field parallel to the piston field a very rapid magnetic diffusion of the piston field occurs. With an antiparallel bias field less rapid magnetic penetration occurs, but still it is greater than is implied by the equilibrium, stable plasma conductivity. It has been conjectured that electron energy loss along the magnetic field lines occurs in the parallel field case and electron energy containment due to closed field lines occurs in the antiparallel case. Because the effective electron collision frequency, and consequently the magnetic diffusivity, depends on the instability growth rate and turbulence level, the difference in magnetic penetration times could be taken to imply that energy loss along the magnetic field is affecting the detailed nature of the cross field instability. We report here experimental results on X-ray and microwave emission relevant to this problem. The experimental device is a fast, high voltage theta pinch [3] . The plasma radius is 7.6 cm and the length of the theta coil is 50 cm. For our initial conditions (hydrogen plasma, n, = 1 X 1013 cm-3,Bz=?l kG)
* Supported by the Defense Nuclear Agency.
the applied piston field results in an azimuthal electron drift velocity ud, as determined from magnetic field profiles, which is greater than the initial electron thermal velocity (~m,u~;r. 100 eV, KT, = 2 eV). l’his has lead us to believe that initially we have a streaming electron plasma wave instability with linear growth rates and frequencies m (me/mi)“3 ape [4] . One expects that this would heat the electrons to the drift energy turning off this mode of instability and allowing a beam cyclotron or ion acoustic instability to dominate [S, 6,7] . Heating of the electrons has been inferred from the X-ray spectrum. The detector was a photomultiplier, plastic scintillator, thin foil combination which received photons from the entire volume of the plasma column. In the parallel field situation the measurements indicate an electron temperature of 300 eV. For the same applied voltages but with opposite polarity piston and bias fields the electron temperature is 3 keV. Both temperature measurements are for times before the current sheath reaches the axis. A possible conclusion is that the higher temperature (above 300 ev), is due to the second phase instability (e.g., ion acoustic). High temperatures result when the heating rate exceeds the loss rate. We assume that energy loss occurs in the parallel field case at the rate 2V,/Z, whereu, is the electron thermal speed along the magnetic field and 1 is the length of heated plasma (e.e., the coil length). If we take as the heating rate the linear ion acoustic growth rate [5] , r ~ (Rn2e/8mi)1’2 kud/~~l+,(khD)2} 3’2 then ud SE and T, >> Ti the loss rate exceeds the growth rate for KT, = 5 (kitD)(udfie) keV. If at early times in
the ion acoustic phase most of the turbulent energy appears in modes for which kh, < 0.1 then the ion 339
Volume 42A, number 5
I
CENTER
, CIITLR
PHYSICS LETTERS
PARALLEL I
ANTlPARALLEL
.
END
END
1 January 1973
sion at frequencies close to the electron plasma frequency. We have observed the emitted radiation with a 3 cm waveguide detection system. The horn antenna was placed to observe across the plasma column at either a slot in the center of the theta coil or 15 cm from the end of the coil. Polarization of the emitted radiation was observed by rotating the system 90”. Tracings of oscilloscope signals for various polarizations, positions and magnetic field polarities are seen in the figure. Only in the case of parallel fields is an appreciable microwave signal seen at the ends of the theta coil. In addition at this downfield position the signal is polarized by about 4.5 to 1 with electric vector parallel to the plasma cylinder axis. This is probably due to hot electrons travelling along the mag netic field and exciting electron plasma oscillations in the cold plasma. The risetime of the signal may be associated with the time to deplete the volume under the theta coil of hot electrons. This assumption appears to be consistent with the X-ray estimate of 300 eV electron temperature. In conclusion it appears that it is necessary to assume that energy is lost at the electron thermal velocity along the lines of force which implies that the instability rapidly transfers energy along the field lines but is not a significant inhibitor of thermal loss in this direction.
iLisT! 6,
/
h
/
Fig. 1. Microwave diode signals which show the appearance of field alligned electron plasma oscillations outside the theta pinch coil only in the parallel fields configuration. The time scale is 50 nsec/division. The traces on the left have one half the sensitivity of the traces on the right.
acoustic instability will not be able to develop electron temperatures above a few hundred electron volts. Consequently the turbulence level stays high and the electron temperature remains about the same as the electron drift energy due to the high frequency instability being rekindled as the temperature drops. In the antiparallel case the lack of electron energy loss can allow the ion acoustic instability to develop fully. A saturation mechanism for this instability is ion trapping. This is expected [S] to occur when KT, % (5/16)2 mi”~/ (1 +(ktX,)2}4. For im,ui e x 100 eV and for taking ktXD = 1 for the trapping mode we find that trapping occurs for KT, m 2.5 keV shutting off the rapid heating. These theoretical results appear to be consistent with our observations. The difference between the parallel and antiparallel cases is also apparent from the microwave emis-
340
References [ 1) G.C. Goldenbaum, Phys. Fluids 10 (1967) 1897. [ 21 A.W. DeSilva et al., Phys. Fluids 14 (1971) 42. [3] [4] [5] [ 61
G.C. Goldenbaum et al., Phys. Fluids 15 (1971) 1491. 0. Buneman, Phys. Rev. 115 (1959) 503. M. Lampe et al., Phys. Rev. Lett. 26 (1971) 1221. D. Biskamp and R. Chodura, Plasma physics and controlled nuclear fusion research 197 1 (International atomic energy agency, Vienna, 1971) II, p. 265. [ 71 D. Forslund, R. Morse and C. Nielson, ibid., p. 277.
Volume 42A, number 5
1 January 1973
ENERGY LOSS EFFECTS ON TURBULENT HEATING* K.A. GERBER and G.C. GOLDENBAUM Naval Research Laboratory, Washington, D.C. 20390, USA Received 14 November 1972
Experimental evidence is presented for the effect of electron energy loss on determining the type of cross field electron streaming instability that develops in low density, high temperature plasmas.
Plasma instabilities involving electrons streaming with respect to ions across magnetic field lines have received a great deal of attention in the last few years. The interpretation of some experimental investigations of plasma heating based on these instabilities has been complicated because of the possibility of electron energy loss along the magnetic field lines [ 1,2] . The experiments we refer to involve low density theta pinches. It has been found that when the theta pinch is operated without an initial bias magnetic field or ‘with a bias field parallel to the piston field a very rapid magnetic diffusion of the piston field occurs. With an antiparallel bias field less rapid magnetic penetration occurs, but still it is greater than is implied by the equilibrium, stable plasma conductivity. It has been conjectured that electron energy loss along the magnetic field lines occurs in the parallel field case and electron energy containment due to closed field lines occurs in the antiparallel case. Because the effective electron collision frequency, and consequently the magnetic diffusivity, depends on the instability growth rate and turbulence level, the difference in magnetic penetration times could be taken to imply that energy loss along the magnetic field is affecting the detailed nature of the cross field instability. We report here experimental results on X-ray and microwave emission relevant to this problem. The experimental device is a fast, high voltage theta pinch [3] . The plasma radius is 7.6 cm and the length of the theta coil is 50 cm. For our initial conditions (hydrogen plasma, n, = 1 X 1013 cm-3,Bz=?l kG)
* Supported by the Defense Nuclear Agency.
the applied piston field results in an azimuthal electron drift velocity ud, as determined from magnetic field profiles, which is greater than the initial electron thermal velocity (~m,u~;r. 100 eV, KT, = 2 eV). l’his has lead us to believe that initially we have a streaming electron plasma wave instability with linear growth rates and frequencies m (me/mi)“3 ape [4] . One expects that this would heat the electrons to the drift energy turning off this mode of instability and allowing a beam cyclotron or ion acoustic instability to dominate [S, 6,7] . Heating of the electrons has been inferred from the X-ray spectrum. The detector was a photomultiplier, plastic scintillator, thin foil combination which received photons from the entire volume of the plasma column. In the parallel field situation the measurements indicate an electron temperature of 300 eV. For the same applied voltages but with opposite polarity piston and bias fields the electron temperature is 3 keV. Both temperature measurements are for times before the current sheath reaches the axis. A possible conclusion is that the higher temperature (above 300 ev), is due to the second phase instability (e.g., ion acoustic). High temperatures result when the heating rate exceeds the loss rate. We assume that energy loss occurs in the parallel field case at the rate 2V,/Z, whereu, is the electron thermal speed along the magnetic field and 1 is the length of heated plasma (e.e., the coil length). If we take as the heating rate the linear ion acoustic growth rate [5] , r ~ (Rn2e/8mi)1’2 kud/~~l+,(khD)2} 3’2 then ud SE and T, >> Ti the loss rate exceeds the growth rate for KT, = 5 (kitD)(udfie) keV. If at early times in
the ion acoustic phase most of the turbulent energy appears in modes for which kh, < 0.1 then the ion 339
Volume 42A, number 5
I
CENTER
, CIITLR
PHYSICS LETTERS
PARALLEL I
ANTlPARALLEL
.
END
END
1 January 1973
sion at frequencies close to the electron plasma frequency. We have observed the emitted radiation with a 3 cm waveguide detection system. The horn antenna was placed to observe across the plasma column at either a slot in the center of the theta coil or 15 cm from the end of the coil. Polarization of the emitted radiation was observed by rotating the system 90”. Tracings of oscilloscope signals for various polarizations, positions and magnetic field polarities are seen in the figure. Only in the case of parallel fields is an appreciable microwave signal seen at the ends of the theta coil. In addition at this downfield position the signal is polarized by about 4.5 to 1 with electric vector parallel to the plasma cylinder axis. This is probably due to hot electrons travelling along the mag netic field and exciting electron plasma oscillations in the cold plasma. The risetime of the signal may be associated with the time to deplete the volume under the theta coil of hot electrons. This assumption appears to be consistent with the X-ray estimate of 300 eV electron temperature. In conclusion it appears that it is necessary to assume that energy is lost at the electron thermal velocity along the lines of force which implies that the instability rapidly transfers energy along the field lines but is not a significant inhibitor of thermal loss in this direction.
iLisT! 6,
/
h
/
Fig. 1. Microwave diode signals which show the appearance of field alligned electron plasma oscillations outside the theta pinch coil only in the parallel fields configuration. The time scale is 50 nsec/division. The traces on the left have one half the sensitivity of the traces on the right.
acoustic instability will not be able to develop electron temperatures above a few hundred electron volts. Consequently the turbulence level stays high and the electron temperature remains about the same as the electron drift energy due to the high frequency instability being rekindled as the temperature drops. In the antiparallel case the lack of electron energy loss can allow the ion acoustic instability to develop fully. A saturation mechanism for this instability is ion trapping. This is expected [S] to occur when KT, % (5/16)2 mi”~/ (1 +(ktX,)2}4. For im,ui e x 100 eV and for taking ktXD = 1 for the trapping mode we find that trapping occurs for KT, m 2.5 keV shutting off the rapid heating. These theoretical results appear to be consistent with our observations. The difference between the parallel and antiparallel cases is also apparent from the microwave emis-
340
References [ 1) G.C. Goldenbaum, Phys. Fluids 10 (1967) 1897. [ 21 A.W. DeSilva et al., Phys. Fluids 14 (1971) 42. [3] [4] [5] [ 61
G.C. Goldenbaum et al., Phys. Fluids 15 (1971) 1491. 0. Buneman, Phys. Rev. 115 (1959) 503. M. Lampe et al., Phys. Rev. Lett. 26 (1971) 1221. D. Biskamp and R. Chodura, Plasma physics and controlled nuclear fusion research 197 1 (International atomic energy agency, Vienna, 1971) II, p. 265. [ 71 D. Forslund, R. Morse and C. Nielson, ibid., p. 277.