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Electromagnetic radiation originating from unstable electron oscillations
Volume 55A, number 2
PHYSICS LETTERS
17 November 1975
ELECTROMAGNETIC RADIATION ORIGINATING FROM UNSTABLE ELECTRON OSCILLATIONS J.J. RASMUSSEN and H.L. PECSELI Association Euratom - Danish AEK, Physics Department A E K Ris~, DK-4000 Roskilde, Denmark
Received 23 September 1975 Electromagnetic oscillations in the range 300 - 700 MHz were observed from an unmagnetized argon discharge with an unstable electron velocity distribution function.
The experiment was carried out in the discharge shown schematically on fig. 1. (A somewhat similar device is described in ref. [ 1]). The plasma was created by ionization of the neutral gas (Ar) by fast electrons emitted from the negatively biased cathode and accelerated through the sheet towards the grounded grid. The electron velocity distribution between the grid and the movable, conducting end-plate consisted of two components: uncolliding fast electrons emitted from the cathode and a group of thermal electrons produced by the ionizations [2]. The two shielded Langrnuir probes shown on fig. 1 allowed investigation of both components. The density, n, of the thermal component is 109 - 1010 cm -3 (depending on neutral pressure and discharge current) and its temperature T "" 3 - 4 eV. The density, n, varied roughly linearly with the discharge current for fixed neutral pressure. The beam density, nb, was estimated to be n b " n X 10 -2. and the beam temperature Tb "- 2T.
/ I
F'X'7 /110n Fig. 1. Schematic diagram of experimental set-up.
The beam velocity Vb was given by the difference between the cathode bias ¢c and the plasma potential Cp. In our experimental conditions ¢p ~ - 5 V. The electron distribution is unstable for sufficiently high Vb [e.g. 3]. Spontaneous oscillations in the plasma were detected by an ordinary Langmuir probe (not shown on fig. 1). The oscillations showed a radial increase in amplitude and thus appeared as surface waves. Electromagnetic oscillations outside the plasma were detected on a halfwave dipole antenna using a Hewlett Packard spectrum analyzer. The radiation appeared simultaneously with the enhanced oscillations in the plasma. When the discharge was surrounded by a grounded metal cage, we observed a decrease in the amplitude of the electromagnetic oscillations by a factor of ~ 50, thus ensuring that the oscillations did originate from the plasma [4]. The electromagnetic oscillations were polarized parallel to the discharge axis and the radiation pattern was in all cases investigated, symmetric with respect to a plane perpendicular to the discharge axis. We interpret the radiation as being due to standing, m = 0, electron surface oscillations spontaneously excited due to the unstable electron distribution. Only waves travelling from the grid towards the end-plate are unstable. Reflections at the steep density profiles at the endplate and grid give rise to a standing wave (or rather a standing component). Seen from the far field a standing wave of N wavelengths may be viewed as an array of N oscillating dipoles orientated along the axis, and it will radiate accordingly (although slow surface waves are "non-radiating"). By carefully adjusting the movable end-plate and the discharge current, we obtained radiation patterns with 2 or 3 main 85
Volume 55A, number 2
PHYSICS LETTERS
i~" (Qrb. units)
; I ......II f L: lOcm, PAr = 2 x lO-3mrnHg k ~..L.
I
4
I
5
I
I
6 x 102rri I
Fig. 2. Normalized frequency s2/x/~ for various ft/V b as explained in the text. The length of the plasma column is L = 10 cm and the neutral argon pressure is 2 × 10 -3 mm ttg. The mean free path for electron-argon collisions is ~ 20 cm. lobes corresponding to 2 or 3 wavelenghts. For 4 or more wavelengths the radiation pattern became somewhat irregular. In our case the real part of the dispersion relation Rew = ~ = ~ ( k ) for the oscillations is determined by the thermal electon comporient, while the beam determines lm6o since n h ~ n. (If we, for instance assume T ~ 0, n ~ const., and quasistationarity, then ~ 2 ( k ) = W2 Im(ka)Km(ka)ka, where a is the tube radius, and I m and K m the modified Bessel and Hankel functions respectively.) The most unstable wave corresponds to the wave-number where the dielectric function of the beam alone is zero, since this case gives the strongest modification of the electron-electron interaction, i.e. ~ ( k ) - k Vb = 6dpb ~ 0 (¢Opb is the plasma frequency of the beam; Ogpb "~ £2). In fig. 2 we show ~/x/n (in arbitrary units) as a function of k = ~2/Vb. (This k-value will generally be larger than or equal to the k-value of the oscilla-
86
17 November 1975
tions since the most unstable oscillation need not satisfy the standing wave condition: k = 21r/NL where L is defined on fig. 1). Assuming that we observe the most unstable standing wave, we may interpret fig. 2 as showing the dispersion relation for the oscillations. ~2/x/n ~ ~2/~p is independent o f k in agreement with calculated and measured dispersion relations for electron surface oscillations for short wavelenghts [ 5 - 6 ] . The absolute magnitude of ~2 agrees favorably with the predicted value of [ 5 - 6 ] using the average density measured by the Langmuir probe. We attribute the line width of the oscillations (indicated on fig. 2) to the effect of the unstable oscillations with smaller growth rates. Sporadic signals originating from standing waves between the grid and the cathode were also observed. Our explanation applies equally well to these signals. We thank N. D'Angelo for suggesting the experiment and N. Sato for valuable discussions. The skilled technical assistance of M. Nielsen and B. Reher is acknowledged.
References
[1] Y. Nakamura, J. Phys. Soc. Japan 28 (1970) 1315.
[2] J.J. Rasmussen and H.L. I~cseli, Ris~ M-1818 (to be published). [3] R.J. Briggs, in Advances in Plasma Physics Vol. 4, eds. A. Symon and W.B. Thompson (Interscience 1971) p.43. [4] ICG. Emeleus and A. Garscadden, Naturwissensehaften 47 (1960) 491.
[5] A.W. Trivelpiece and R.W. Gould, J. Appl. Phys. 30 (1959) 1784. [6] B.B. O'Brien, Plasma Phys. 9 (1967) 369.
PHYSICS LETTERS
17 November 1975
ELECTROMAGNETIC RADIATION ORIGINATING FROM UNSTABLE ELECTRON OSCILLATIONS J.J. RASMUSSEN and H.L. PECSELI Association Euratom - Danish AEK, Physics Department A E K Ris~, DK-4000 Roskilde, Denmark
Received 23 September 1975 Electromagnetic oscillations in the range 300 - 700 MHz were observed from an unmagnetized argon discharge with an unstable electron velocity distribution function.
The experiment was carried out in the discharge shown schematically on fig. 1. (A somewhat similar device is described in ref. [ 1]). The plasma was created by ionization of the neutral gas (Ar) by fast electrons emitted from the negatively biased cathode and accelerated through the sheet towards the grounded grid. The electron velocity distribution between the grid and the movable, conducting end-plate consisted of two components: uncolliding fast electrons emitted from the cathode and a group of thermal electrons produced by the ionizations [2]. The two shielded Langrnuir probes shown on fig. 1 allowed investigation of both components. The density, n, of the thermal component is 109 - 1010 cm -3 (depending on neutral pressure and discharge current) and its temperature T "" 3 - 4 eV. The density, n, varied roughly linearly with the discharge current for fixed neutral pressure. The beam density, nb, was estimated to be n b " n X 10 -2. and the beam temperature Tb "- 2T.
/ I
F'X'7 /110n Fig. 1. Schematic diagram of experimental set-up.
The beam velocity Vb was given by the difference between the cathode bias ¢c and the plasma potential Cp. In our experimental conditions ¢p ~ - 5 V. The electron distribution is unstable for sufficiently high Vb [e.g. 3]. Spontaneous oscillations in the plasma were detected by an ordinary Langmuir probe (not shown on fig. 1). The oscillations showed a radial increase in amplitude and thus appeared as surface waves. Electromagnetic oscillations outside the plasma were detected on a halfwave dipole antenna using a Hewlett Packard spectrum analyzer. The radiation appeared simultaneously with the enhanced oscillations in the plasma. When the discharge was surrounded by a grounded metal cage, we observed a decrease in the amplitude of the electromagnetic oscillations by a factor of ~ 50, thus ensuring that the oscillations did originate from the plasma [4]. The electromagnetic oscillations were polarized parallel to the discharge axis and the radiation pattern was in all cases investigated, symmetric with respect to a plane perpendicular to the discharge axis. We interpret the radiation as being due to standing, m = 0, electron surface oscillations spontaneously excited due to the unstable electron distribution. Only waves travelling from the grid towards the end-plate are unstable. Reflections at the steep density profiles at the endplate and grid give rise to a standing wave (or rather a standing component). Seen from the far field a standing wave of N wavelengths may be viewed as an array of N oscillating dipoles orientated along the axis, and it will radiate accordingly (although slow surface waves are "non-radiating"). By carefully adjusting the movable end-plate and the discharge current, we obtained radiation patterns with 2 or 3 main 85
Volume 55A, number 2
PHYSICS LETTERS
i~" (Qrb. units)
; I ......II f L: lOcm, PAr = 2 x lO-3mrnHg k ~..L.
I
4
I
5
I
I
6 x 102rri I
Fig. 2. Normalized frequency s2/x/~ for various ft/V b as explained in the text. The length of the plasma column is L = 10 cm and the neutral argon pressure is 2 × 10 -3 mm ttg. The mean free path for electron-argon collisions is ~ 20 cm. lobes corresponding to 2 or 3 wavelenghts. For 4 or more wavelengths the radiation pattern became somewhat irregular. In our case the real part of the dispersion relation Rew = ~ = ~ ( k ) for the oscillations is determined by the thermal electon comporient, while the beam determines lm6o since n h ~ n. (If we, for instance assume T ~ 0, n ~ const., and quasistationarity, then ~ 2 ( k ) = W2 Im(ka)Km(ka)ka, where a is the tube radius, and I m and K m the modified Bessel and Hankel functions respectively.) The most unstable wave corresponds to the wave-number where the dielectric function of the beam alone is zero, since this case gives the strongest modification of the electron-electron interaction, i.e. ~ ( k ) - k Vb = 6dpb ~ 0 (¢Opb is the plasma frequency of the beam; Ogpb "~ £2). In fig. 2 we show ~/x/n (in arbitrary units) as a function of k = ~2/Vb. (This k-value will generally be larger than or equal to the k-value of the oscilla-
86
17 November 1975
tions since the most unstable oscillation need not satisfy the standing wave condition: k = 21r/NL where L is defined on fig. 1). Assuming that we observe the most unstable standing wave, we may interpret fig. 2 as showing the dispersion relation for the oscillations. ~2/x/n ~ ~2/~p is independent o f k in agreement with calculated and measured dispersion relations for electron surface oscillations for short wavelenghts [ 5 - 6 ] . The absolute magnitude of ~2 agrees favorably with the predicted value of [ 5 - 6 ] using the average density measured by the Langmuir probe. We attribute the line width of the oscillations (indicated on fig. 2) to the effect of the unstable oscillations with smaller growth rates. Sporadic signals originating from standing waves between the grid and the cathode were also observed. Our explanation applies equally well to these signals. We thank N. D'Angelo for suggesting the experiment and N. Sato for valuable discussions. The skilled technical assistance of M. Nielsen and B. Reher is acknowledged.
References
[1] Y. Nakamura, J. Phys. Soc. Japan 28 (1970) 1315.
[2] J.J. Rasmussen and H.L. I~cseli, Ris~ M-1818 (to be published). [3] R.J. Briggs, in Advances in Plasma Physics Vol. 4, eds. A. Symon and W.B. Thompson (Interscience 1971) p.43. [4] ICG. Emeleus and A. Garscadden, Naturwissensehaften 47 (1960) 491.
[5] A.W. Trivelpiece and R.W. Gould, J. Appl. Phys. 30 (1959) 1784. [6] B.B. O'Brien, Plasma Phys. 9 (1967) 369.