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Off axis helicon amplification
Solid State Communications Vol. 4, PP. 377 -380, 1966. Pergamon Press Ltd. Printed in Great Britain.
OFF AXIS HELICON AMPLIFICATION A. C. Baynham and P. W. Braddock Royal Radar Establishment, Malvern, Worcs. Engiand (Received 28 April 1966 by G. G. Macfarlane)
When the helicon propagates at an angle to the applied magnetic field, a longitudinal electric field component is introduced. The possibility of using this feature to amplify helicons is discussed, and experimental evidence of electric field induced changes in the imaginary part of the propagation vector presented.
THE HELICON is a purely transverse electromagnetic wave, when propagating parallel to the applied magnetic field B0. However, if the propagation vector is inclined at a small angle to B0 a longitudinal electric field component is introduced, electrons tend to become trapped in the potential troughs, and the wave is damped. 1 If an inversion of the free carrier velocity dis tribution function can be achieved in the neighbourhood of the helicon phase velocity, negative damping, or gain may be expected. One method of approaching such a situation is by applying a d. c. electric field pulse parallel to the helicon propagation vector. We report here the successful observation of off axis helicon growth in the presence of an electric field. This mechanism should be of distinguished 2 type amplification from the where Bok and system, theNoziere helicon is coupled to the drifting free carrier system by the Lorentz V x B term. The coupling discussed in this communication arises through the longitudinal electric field component characteristic of off axis helicon propagation,
-________________________
fr;’
~.
~“
FIG. 1
The experimental work has been performed at liquid nitrogen temperature using indium antimonide with a free carrier concentration of 1016/cm3. Coupling to the helicon system is achieved through the sides of the specimen using coils thus leaving the ends free for the application of electric field contacts, Two observational systems have been used, 377
A. Shows helicon growth within an electric field pulse of 5 ~ sec duration. B. Shows the switch on response of the gated amplifier. In the first a continuous r. f. signal is applied to the launching coil. The signal at the output coil is observed on an oscilloscope after passing through a gated amplifier, which is switched off
378
OFF AXIS HELICON AMPLIFICATION
during the rise and fall of the electric field pulse. A typical observation is shown in Figure 1(A). The second observational system which has been employed dispenses with the gated amplifier. An r. f. source is arranged to excite pulses of helicons inside and outside the applied electric field pulse. Although there is appreciable leakage of signal between launching and detecting coils with this system the results are in agreement with those obtained using the gated amplifier. Measurements at a constant electric field show that maximum helicon growth is achieved when the propagation vector is inclined at an angle of 250 to the magnetic field axis. A study of the growth as a function of electric field strength using a constant magnetic field inclined at 20° to the direction of propagation yields the results plotted in Fig. 2. Here growth is defined as the
‘4
Vol. 4, No. 8
applied to the off axis helicon system, a change occurs in both real and imaginary parts of the dispersion relation. Thus in addition to the helicon amplification of interest here, an electric field induced phase change in the detected signal must be expected. Consequently a field induced change in helicon signal strength may arise from amplification, or the modified interference of signal and breakthrough. If the electric field merely changes the real part of dispersion relation, its effeet should occur in a time of order; (Specimen length/ Helicon velocity). Thus the example of growth shown in Figure 1 which occurs over a period of 5 .isec although the signal transit time is 0. 05 ~sec, indicates that helicon growth must be occuring.
A quantitative distinction between these two processes is possible, if the growth is stud-
ted as a function of magneitc field. In Fig. 3 the
-
~
I’2-
~,
i’C
-
50
I 100
150
200
FIELD ON SPECIMEN
[~lts cm’]
0’S FIG. 2
Helicon growth as a function of electric field strength, with a constant magnetic field of 6 kG inclined at 200 to the propagation direction. atio of the helicon signal amplitude inside and outside the electric field pulse. The interpretation of this data must be made with some care. When a drift field is
off axis helicon signal amplitude is plotted against magnetic field, with and without a drift field. The behaviour is most easily described using the diagramatic inset in Fig. 3. Here the overall detected signal is represented by the vector sum of the
Vol. 4, No. 8
OFF AXIS HELICON AMPLIFICATION VARIATION OF I’ELICON SIGNAL WITH MAGNETIC FIELD USING AN InSb SPECIMEN AT 77°K
379 -
.8
C
2
FIELD
[kGauss]
FIG. 3
Helicon signal as a function of magnetic field with and without an electric field. finite leakage signal signal between source and detecting coils “oA”, and the helicon signal “oB~’ In the absence of an electric field pulse, a single spiral describes the helicon amplitude and phase as a function of magnetic field, and an oscillatary signal is detected as the magnetic field is increased. If a drift field merely introduces a phase change, a similar pattern is traced, though displaced along the magnetic field axis. In contrast, helicon growth implies a magnified spiral, which changes the amplitude of the signal tions as only a function of magnetic field. Theoscil]aexperimental results plotted in Fig. 3 provide evidence of electric field induced amplitude and phase effects. They are indicative of helicon growth at magnetic fields below 8. 3 kG and increased attenuation at higher magnetic fields; a result which is in-keeping with that shown in Fig. 2, since either increased magnetic fields, or decreased electric fields serve to reduce the ratio of the electron drift velocity to helicon phase velocity,
tion, and allowing for carrier bunching consistent with current continuity have been obtained. They predict helicon instability when the drift velocity exceeds a critical value. The minimum electric field necessary for the onset of amplification is predicted when the propagation vector is indined at an angle e, of 18°tothe magnetic field axis; experimentally a value of e = 25°isobtained. Using a similar field configuration micro-wave emission has been observed from indium antim3 which may well be some form of amplified onide noise.4 Here too the minimum threshold field occurs for an inclination of about 20°between electric and magnetic fields.
A formal theoretical treatment of helicon amplification using the off axis coupling mechanism is at present being performed. Preliminary solutions using the quasi static limit approxima-
In this communication experimental evidence that an electric field effects both real and imaginary parts of the off axis helicon wave vector has been presented. Particular attention
Modification of the theory to exclude this approximation when B = 0 is fairly easy, yielding the on axis gain term in accordance with Bok and Noziere. However, when B ~ 0 additional complications arise which have not as yet allowed a non quasi static treatment of off axis propagation to be performed.
380
OFF AXIS HELICON AMPLIFICATION
has been directed to the imaginary component, which can be either increased or reduced by suitably chosen electric fields. The possibility of achieving net gain using this coupling between off axis helicons, and a drifted (extrinsic or intrtnsic) plasma will be discussed in a later publicatlon. However, a very much simplified theoretical analysis of this effect predicts an
Vol. 4, No. 8
angular dependence of the threshold field for onset of amplification, which is in approximate agreement with experiment. British Crown Copyright. Reproduction by permission of the Controller, Her Britannic Majesty’s Stationary Office.
References 1. LANDAU L., Soviet Physics, J.E.T.P.
16, 574 (1946),
2. BOK J. and NOZIERES P., J. Phys. Chem. Sol. 24, 709 (1963). 3. LARRABEE R. D. and HICINBOTHEM W. A. Jr. Plasma Effects in Solids, 7th mt. ConI, on Physics of Semiconductors (1964). 4. STEELE M. C. Plasma Effectsin Solids, 7th mt. Conf. on Physics of Semiconductors (1964).
Quand le vecteur d’onde d’un helicon et le champ magnetique ne sant pas parallel, un champ électrique longitudinal s’est produs. On discute Ia possibilité de l’utilisatton de ce champ pour amplification, et 1’ evidence experimental pour changes de la partie imaginaire du vecteur d’ onde avec champ ~lectrique est presenti.
OFF AXIS HELICON AMPLIFICATION A. C. Baynham and P. W. Braddock Royal Radar Establishment, Malvern, Worcs. Engiand (Received 28 April 1966 by G. G. Macfarlane)
When the helicon propagates at an angle to the applied magnetic field, a longitudinal electric field component is introduced. The possibility of using this feature to amplify helicons is discussed, and experimental evidence of electric field induced changes in the imaginary part of the propagation vector presented.
THE HELICON is a purely transverse electromagnetic wave, when propagating parallel to the applied magnetic field B0. However, if the propagation vector is inclined at a small angle to B0 a longitudinal electric field component is introduced, electrons tend to become trapped in the potential troughs, and the wave is damped. 1 If an inversion of the free carrier velocity dis tribution function can be achieved in the neighbourhood of the helicon phase velocity, negative damping, or gain may be expected. One method of approaching such a situation is by applying a d. c. electric field pulse parallel to the helicon propagation vector. We report here the successful observation of off axis helicon growth in the presence of an electric field. This mechanism should be of distinguished 2 type amplification from the where Bok and system, theNoziere helicon is coupled to the drifting free carrier system by the Lorentz V x B term. The coupling discussed in this communication arises through the longitudinal electric field component characteristic of off axis helicon propagation,
-________________________
fr;’
~.
~“
FIG. 1
The experimental work has been performed at liquid nitrogen temperature using indium antimonide with a free carrier concentration of 1016/cm3. Coupling to the helicon system is achieved through the sides of the specimen using coils thus leaving the ends free for the application of electric field contacts, Two observational systems have been used, 377
A. Shows helicon growth within an electric field pulse of 5 ~ sec duration. B. Shows the switch on response of the gated amplifier. In the first a continuous r. f. signal is applied to the launching coil. The signal at the output coil is observed on an oscilloscope after passing through a gated amplifier, which is switched off
378
OFF AXIS HELICON AMPLIFICATION
during the rise and fall of the electric field pulse. A typical observation is shown in Figure 1(A). The second observational system which has been employed dispenses with the gated amplifier. An r. f. source is arranged to excite pulses of helicons inside and outside the applied electric field pulse. Although there is appreciable leakage of signal between launching and detecting coils with this system the results are in agreement with those obtained using the gated amplifier. Measurements at a constant electric field show that maximum helicon growth is achieved when the propagation vector is inclined at an angle of 250 to the magnetic field axis. A study of the growth as a function of electric field strength using a constant magnetic field inclined at 20° to the direction of propagation yields the results plotted in Fig. 2. Here growth is defined as the
‘4
Vol. 4, No. 8
applied to the off axis helicon system, a change occurs in both real and imaginary parts of the dispersion relation. Thus in addition to the helicon amplification of interest here, an electric field induced phase change in the detected signal must be expected. Consequently a field induced change in helicon signal strength may arise from amplification, or the modified interference of signal and breakthrough. If the electric field merely changes the real part of dispersion relation, its effeet should occur in a time of order; (Specimen length/ Helicon velocity). Thus the example of growth shown in Figure 1 which occurs over a period of 5 .isec although the signal transit time is 0. 05 ~sec, indicates that helicon growth must be occuring.
A quantitative distinction between these two processes is possible, if the growth is stud-
ted as a function of magneitc field. In Fig. 3 the
-
~
I’2-
~,
i’C
-
50
I 100
150
200
FIELD ON SPECIMEN
[~lts cm’]
0’S FIG. 2
Helicon growth as a function of electric field strength, with a constant magnetic field of 6 kG inclined at 200 to the propagation direction. atio of the helicon signal amplitude inside and outside the electric field pulse. The interpretation of this data must be made with some care. When a drift field is
off axis helicon signal amplitude is plotted against magnetic field, with and without a drift field. The behaviour is most easily described using the diagramatic inset in Fig. 3. Here the overall detected signal is represented by the vector sum of the
Vol. 4, No. 8
OFF AXIS HELICON AMPLIFICATION VARIATION OF I’ELICON SIGNAL WITH MAGNETIC FIELD USING AN InSb SPECIMEN AT 77°K
379 -
.8
C
2
FIELD
[kGauss]
FIG. 3
Helicon signal as a function of magnetic field with and without an electric field. finite leakage signal signal between source and detecting coils “oA”, and the helicon signal “oB~’ In the absence of an electric field pulse, a single spiral describes the helicon amplitude and phase as a function of magnetic field, and an oscillatary signal is detected as the magnetic field is increased. If a drift field merely introduces a phase change, a similar pattern is traced, though displaced along the magnetic field axis. In contrast, helicon growth implies a magnified spiral, which changes the amplitude of the signal tions as only a function of magnetic field. Theoscil]aexperimental results plotted in Fig. 3 provide evidence of electric field induced amplitude and phase effects. They are indicative of helicon growth at magnetic fields below 8. 3 kG and increased attenuation at higher magnetic fields; a result which is in-keeping with that shown in Fig. 2, since either increased magnetic fields, or decreased electric fields serve to reduce the ratio of the electron drift velocity to helicon phase velocity,
tion, and allowing for carrier bunching consistent with current continuity have been obtained. They predict helicon instability when the drift velocity exceeds a critical value. The minimum electric field necessary for the onset of amplification is predicted when the propagation vector is indined at an angle e, of 18°tothe magnetic field axis; experimentally a value of e = 25°isobtained. Using a similar field configuration micro-wave emission has been observed from indium antim3 which may well be some form of amplified onide noise.4 Here too the minimum threshold field occurs for an inclination of about 20°between electric and magnetic fields.
A formal theoretical treatment of helicon amplification using the off axis coupling mechanism is at present being performed. Preliminary solutions using the quasi static limit approxima-
In this communication experimental evidence that an electric field effects both real and imaginary parts of the off axis helicon wave vector has been presented. Particular attention
Modification of the theory to exclude this approximation when B = 0 is fairly easy, yielding the on axis gain term in accordance with Bok and Noziere. However, when B ~ 0 additional complications arise which have not as yet allowed a non quasi static treatment of off axis propagation to be performed.
380
OFF AXIS HELICON AMPLIFICATION
has been directed to the imaginary component, which can be either increased or reduced by suitably chosen electric fields. The possibility of achieving net gain using this coupling between off axis helicons, and a drifted (extrinsic or intrtnsic) plasma will be discussed in a later publicatlon. However, a very much simplified theoretical analysis of this effect predicts an
Vol. 4, No. 8
angular dependence of the threshold field for onset of amplification, which is in approximate agreement with experiment. British Crown Copyright. Reproduction by permission of the Controller, Her Britannic Majesty’s Stationary Office.
References 1. LANDAU L., Soviet Physics, J.E.T.P.
16, 574 (1946),
2. BOK J. and NOZIERES P., J. Phys. Chem. Sol. 24, 709 (1963). 3. LARRABEE R. D. and HICINBOTHEM W. A. Jr. Plasma Effects in Solids, 7th mt. ConI, on Physics of Semiconductors (1964). 4. STEELE M. C. Plasma Effectsin Solids, 7th mt. Conf. on Physics of Semiconductors (1964).
Quand le vecteur d’onde d’un helicon et le champ magnetique ne sant pas parallel, un champ électrique longitudinal s’est produs. On discute Ia possibilité de l’utilisatton de ce champ pour amplification, et 1’ evidence experimental pour changes de la partie imaginaire du vecteur d’ onde avec champ ~lectrique est presenti.