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Observation of flux-limited heat flow in a double plasma device
Volume 85A, number 4
OBSERVATION
28 September 1981
PHYSICS LETTERS
OF FLUX-LIMITED
HEAT FLOW IN A DOUBLE PLASMA DEVICE
P.A.C. MOORE ’ and H. MOT2 2 Department
of Engineering
Science,
University of Oxford, Oxford, UK
Received 11 May 1981
Experiments in a double plasma device study the electron velocity distribution and heat flow in large temperature gradients. The heat flow corresponds to a flux-limiting parameter of 0.09 + 0.04.
In laser fusion experiments the heat is conducted from the absorption layer across a region with a temperature gradient which has a scale length L 5 A,where X is the electron mean free path. It has been pointed out by Bickerton [l] that the classical theory of heat conduction is not applicable and various authors [2] have attempted to determine the resulting flux limitation. This letter describes a new approach: the study of electron heat flux in a large temperature gradient in a double plasma (DP) device. Experiments were performed in a cylindrical DP device [3] with 572 ceramic magnets stacked in two layers outside the chamber to give line cusps [4] along the side walls for partial multipole confinement [5] (fig. 1). A discharge (typically 50 V, 50 mA) was created in argon (x10 mPa, 1OW4Torr) by thermionic emission of electrons from up to four tantalum filaments (length 80 mm, diameter 0.2 mm). Two plasmas were formed at the same plasma potential and electron concentration (1014 mm3) with their electrons separated by a negatively biased central grid. The grid consisted of 25 pm diameter copper wires at 1 mm spacing over a hole of diameter 102 mm in a Pyrex glass plate. Electrons in the “hot” plasma (8 eV) on one side of the grid were heated relative to those in the “cold” plasma (3 eV) on the other side by “demon heating”, the selective absorption of low energy electrons by ’ Present address: BP International Ltd, Britannic House, London EC2Y 9BU, UK. 2 Present address: Department of Physics, University of Oxford OX1 3PU, UK.
0 031-9163/81/0000-0000/$02.75
0 1981 North-Holland
mesh
--------------
!-I-!
--------
anod ----
Fig. 1. DP device: chamber diameter 300 mm, F = filament, P = probe.
thin wires at a high voltage [6]. The grid was pulsed to plasma potential in under 10 ns to create a single plasma with a large temperature gradient (X/Lw 500). This caused a thermal wave of hot electrons to flow into the cold plasma. Steady state plasmas and thermal waves were studied by plane Langmuir probes (tantalum, diameter 8 mm). Grid pulses (260 Hz) triggered a sampling oscilloscope connected by a coupling capacitor to the probe in the cold plasma. A signal generator provided a slowly varying probe bias through a low pass falter to give the high frequency component of the probe characteristic at a given time t after the start of the grid pulse. The first derivatives of steady state and high frequency probe characteristics gave the distribution f(u) of the electron velocity component u perpendicular to the probe [7]. Electron concentration and energy were calculated by integration of f(u) and Use, respec225
Volume 85A, number 4
PHYSICS LETTERS
28 September 1981
the time t has to be divided by two in the calculation. This halving of the rate of development of f(u) is believed to be caused by thermoelectric effects, which are excluded from the model. Studies of V, show that a thermal wave moves into the cold plasma and increases V, by 0.9 t 0.2 V, or about 40%. The positions of the midpoint of the wave give its average speed as 0.5 f 0.2 mm ns-I, (5 + 2) X 105 m s-1. The product of the wave’s speed, the concentration of electrons with u > 0 and the increase in electron energy gives the heat flux 4 = 10 f 4 W m-2 This heat flux can be expressed as a fraction f, the flux-limiting parameter, of the dimensional part of a maximum value [9] : q =jNekTe(kT,/m)1/2
0
0.4
0.8
1.2 ”
2.0 1.6 (mm /ns)
Fig. 2. Velocity distribution f(u) at various times for probe 34 mm from grid. Dotted lines: experiment. Full lines: theory, for time half the experimental value of t. Each vertical division 0.1 ns mm-‘.
tively. The corresponding absolute errors were estimated to be 10 and 15%, and were mainly caused by edge effects. Measurements were not possible during the first 40 ns after the grid pulse because of high frequency coupling between grid and probe. Results are presented for an experiment with electron concentration 1.4 X 1Ol4 m-3, Veh = 5 .l V and I’,, = 2.3 V, where veh and V,, are the initial values in the hot and cold plasmas of Fe, the voltage equivalent of the electron temperature T, defined by:
-3 . ;eve=;kTe=;mu
(1)
Fig. 2 shows velocity distributions for various times t at distance x = 34 mm from the grid, where the error bar indicates relative errors only. There are distinct “bumps” in f(u) for small t and “fronts” for large t. Results at 43 mm show similar features, but there are no longer distinct bumps and fronts at 56.5 mm. A theoretical model [8] based on the free streaming of electrons predicts the development of bumps followed by fronts and gives the solid curves in fig. 2. To obtain reasonable agreement with experiments, however, 226
.
(2)
With kTe = e Veh the experimental results give f = 0.09 + 0.04. This lies within the range between f = 0.015 [lo] andf= 1 [ll] which are extreme values found in experiments on plasmas heated by lasers. However these experiments may have involved additional flux limitation by plasma instabilities and spontaneous magnetic fields. In conclusion: experiments in a DP device have studied electron thermal waves in large temperature gradients. Distinct bumps and fronts are observed in the distribution of the electron velocity component parallel to the thermal waves. The heat flux is estimated to correspond to a flux-limiting parameter f = 0.09 + 0.04, within the range observed in plasmas heated by lasers. Further details of this work will be published elsewhere [8]. The first author is grateful for support during this work by the UK Science Research Council and St. John’s College, Oxford. Valuable help was given by Dr. P.T. Rumsby, Dr. R.N. Franklin, Dr. P.J. Barrett and the late Mr. G. Dunmore. The experiment was funded by a contract from Culham Laboratory, EuratomUKAEA Association for Fusion Research. References [l] R.J. Bickerton, Nucl. Fusion 13 (1973) 457. [ 21 W.L. Kruer, Comments Plasma Pbys. 5 (1979) 69. [ 31 R.J. Taylor, K.R. MacKenzie and H. Ikezi, Rev. Sci. Instrum. 43 (1972) 1675.
Volume 85A, number 4
PHYSICS LETTERS
[4] K.N. Leung, T.K. Samec and A. Lamm, Phys. Lett. 51A (1975) 490. [5] R. Limpaecher and K.R. MacKenzie, Rev. Sci. Instrum. 44 (1973) 726. [6] K.R. MacKenzie, R.J. Taylor, D. Cohn, E. Ault and H. Ike& Appl. Phys. Lett. 18 (1971) 529. [7] D. Cr&llon and P.L. Galison, Phys. Fluids 16 (1973) 2180.
28 September 1981
[ 81 P.A.C. Moore, J. Phys. D, to be published. (91 H. Motz, The physics of laser fusion (Academic Press, New York, 1979) p. 153. [lo] D.R. Gray, J.D. Kilkenny,M.S. White,P. BlythandD. Hull, Phys. Rev. Lett. 39 (1977) 1270. [ll] T.P. Donaldson, G.I. Kachen and I.J. Spalding, J. Phys. DlO (1977) 1589.
227
OBSERVATION
28 September 1981
PHYSICS LETTERS
OF FLUX-LIMITED
HEAT FLOW IN A DOUBLE PLASMA DEVICE
P.A.C. MOORE ’ and H. MOT2 2 Department
of Engineering
Science,
University of Oxford, Oxford, UK
Received 11 May 1981
Experiments in a double plasma device study the electron velocity distribution and heat flow in large temperature gradients. The heat flow corresponds to a flux-limiting parameter of 0.09 + 0.04.
In laser fusion experiments the heat is conducted from the absorption layer across a region with a temperature gradient which has a scale length L 5 A,where X is the electron mean free path. It has been pointed out by Bickerton [l] that the classical theory of heat conduction is not applicable and various authors [2] have attempted to determine the resulting flux limitation. This letter describes a new approach: the study of electron heat flux in a large temperature gradient in a double plasma (DP) device. Experiments were performed in a cylindrical DP device [3] with 572 ceramic magnets stacked in two layers outside the chamber to give line cusps [4] along the side walls for partial multipole confinement [5] (fig. 1). A discharge (typically 50 V, 50 mA) was created in argon (x10 mPa, 1OW4Torr) by thermionic emission of electrons from up to four tantalum filaments (length 80 mm, diameter 0.2 mm). Two plasmas were formed at the same plasma potential and electron concentration (1014 mm3) with their electrons separated by a negatively biased central grid. The grid consisted of 25 pm diameter copper wires at 1 mm spacing over a hole of diameter 102 mm in a Pyrex glass plate. Electrons in the “hot” plasma (8 eV) on one side of the grid were heated relative to those in the “cold” plasma (3 eV) on the other side by “demon heating”, the selective absorption of low energy electrons by ’ Present address: BP International Ltd, Britannic House, London EC2Y 9BU, UK. 2 Present address: Department of Physics, University of Oxford OX1 3PU, UK.
0 031-9163/81/0000-0000/$02.75
0 1981 North-Holland
mesh
--------------
!-I-!
--------
anod ----
Fig. 1. DP device: chamber diameter 300 mm, F = filament, P = probe.
thin wires at a high voltage [6]. The grid was pulsed to plasma potential in under 10 ns to create a single plasma with a large temperature gradient (X/Lw 500). This caused a thermal wave of hot electrons to flow into the cold plasma. Steady state plasmas and thermal waves were studied by plane Langmuir probes (tantalum, diameter 8 mm). Grid pulses (260 Hz) triggered a sampling oscilloscope connected by a coupling capacitor to the probe in the cold plasma. A signal generator provided a slowly varying probe bias through a low pass falter to give the high frequency component of the probe characteristic at a given time t after the start of the grid pulse. The first derivatives of steady state and high frequency probe characteristics gave the distribution f(u) of the electron velocity component u perpendicular to the probe [7]. Electron concentration and energy were calculated by integration of f(u) and Use, respec225
Volume 85A, number 4
PHYSICS LETTERS
28 September 1981
the time t has to be divided by two in the calculation. This halving of the rate of development of f(u) is believed to be caused by thermoelectric effects, which are excluded from the model. Studies of V, show that a thermal wave moves into the cold plasma and increases V, by 0.9 t 0.2 V, or about 40%. The positions of the midpoint of the wave give its average speed as 0.5 f 0.2 mm ns-I, (5 + 2) X 105 m s-1. The product of the wave’s speed, the concentration of electrons with u > 0 and the increase in electron energy gives the heat flux 4 = 10 f 4 W m-2 This heat flux can be expressed as a fraction f, the flux-limiting parameter, of the dimensional part of a maximum value [9] : q =jNekTe(kT,/m)1/2
0
0.4
0.8
1.2 ”
2.0 1.6 (mm /ns)
Fig. 2. Velocity distribution f(u) at various times for probe 34 mm from grid. Dotted lines: experiment. Full lines: theory, for time half the experimental value of t. Each vertical division 0.1 ns mm-‘.
tively. The corresponding absolute errors were estimated to be 10 and 15%, and were mainly caused by edge effects. Measurements were not possible during the first 40 ns after the grid pulse because of high frequency coupling between grid and probe. Results are presented for an experiment with electron concentration 1.4 X 1Ol4 m-3, Veh = 5 .l V and I’,, = 2.3 V, where veh and V,, are the initial values in the hot and cold plasmas of Fe, the voltage equivalent of the electron temperature T, defined by:
-3 . ;eve=;kTe=;mu
(1)
Fig. 2 shows velocity distributions for various times t at distance x = 34 mm from the grid, where the error bar indicates relative errors only. There are distinct “bumps” in f(u) for small t and “fronts” for large t. Results at 43 mm show similar features, but there are no longer distinct bumps and fronts at 56.5 mm. A theoretical model [8] based on the free streaming of electrons predicts the development of bumps followed by fronts and gives the solid curves in fig. 2. To obtain reasonable agreement with experiments, however, 226
.
(2)
With kTe = e Veh the experimental results give f = 0.09 + 0.04. This lies within the range between f = 0.015 [lo] andf= 1 [ll] which are extreme values found in experiments on plasmas heated by lasers. However these experiments may have involved additional flux limitation by plasma instabilities and spontaneous magnetic fields. In conclusion: experiments in a DP device have studied electron thermal waves in large temperature gradients. Distinct bumps and fronts are observed in the distribution of the electron velocity component parallel to the thermal waves. The heat flux is estimated to correspond to a flux-limiting parameter f = 0.09 + 0.04, within the range observed in plasmas heated by lasers. Further details of this work will be published elsewhere [8]. The first author is grateful for support during this work by the UK Science Research Council and St. John’s College, Oxford. Valuable help was given by Dr. P.T. Rumsby, Dr. R.N. Franklin, Dr. P.J. Barrett and the late Mr. G. Dunmore. The experiment was funded by a contract from Culham Laboratory, EuratomUKAEA Association for Fusion Research. References [l] R.J. Bickerton, Nucl. Fusion 13 (1973) 457. [ 21 W.L. Kruer, Comments Plasma Pbys. 5 (1979) 69. [ 31 R.J. Taylor, K.R. MacKenzie and H. Ikezi, Rev. Sci. Instrum. 43 (1972) 1675.
Volume 85A, number 4
PHYSICS LETTERS
[4] K.N. Leung, T.K. Samec and A. Lamm, Phys. Lett. 51A (1975) 490. [5] R. Limpaecher and K.R. MacKenzie, Rev. Sci. Instrum. 44 (1973) 726. [6] K.R. MacKenzie, R.J. Taylor, D. Cohn, E. Ault and H. Ike& Appl. Phys. Lett. 18 (1971) 529. [7] D. Cr&llon and P.L. Galison, Phys. Fluids 16 (1973) 2180.
28 September 1981
[ 81 P.A.C. Moore, J. Phys. D, to be published. (91 H. Motz, The physics of laser fusion (Academic Press, New York, 1979) p. 153. [lo] D.R. Gray, J.D. Kilkenny,M.S. White,P. BlythandD. Hull, Phys. Rev. Lett. 39 (1977) 1270. [ll] T.P. Donaldson, G.I. Kachen and I.J. Spalding, J. Phys. DlO (1977) 1589.
227