J. Plasma
J.
Plasma Fusion
Fusion Res.
Res. SERIES,SERIES,Vol.
Vol.6 6(2004)(2004)562–565
000–000

Electron Acceleration due to Electric Field Bursts Closeto the Lower Hybrid Frequency ina High-Voltage Linear Plasma Discharge
TAKEDA Yasumasa and INUZUKA Hiroshi1
1Department of Physics, College of Science and Technology, Nihon University, Tokyo, 101-8308, Japan
Department of Electrical and Electronic Engineering, Faculty of Engineering, Shizuoka University, Hamamatsu, 432-8561, Japan(Received: 9 December 2003 / Accepted: 24 February 2004)

AbstractLower hybrid wave bursts, which were generated in a high-voltage linear plasma discharge, give rise to intenseelectron acceleration evidenced by impulsive hard x-ray fluxes with energies higher than 15 keV detected in thedirection perpendicular to the magnetic field and also in the direction almost parallel to the magnetic field.
The lower hybrid wave packet is more efficient to accelerate high-energy electrons than laminar electric field
pulses such as double layers and localized potential structures.
Keywords:
lower hybrid wave, double layer, transit time acceleration, nonadiabatic electron heating, linear plasma discharge

1. Introduction

2. Experimental apparatus and themethods of measurement

There have been crucial debates and discussion [1] inplasma physics and auroral physics community on thequestion which is more efficient in particle acceleration,
laminar coherent structures such as double layers [2] orlocalized wave structures such as lower hybrid solitary waves[3]?
This paper presents our new findings that electric fieldbursts with frequency in the vicinity of lower hybrid
frequency, which were generated in the initial phase of a highvoltage linear plasma discharge, give rise to intense electronacceleration.
Dependence of the angular distribution of hard x-ray
fluxes on the spectral profile of an originating electric fieldburst is explained according to the theory of transit timeinteraction of a lower hybrid wave [4].
The dominant electron acceleration perpendicular to themagnetic field, which is frequently observed in association
with lower hybrid wave bursts, cannot be understoodaccording to the linear theory of lower hybrid wave. Hencethe recent theory of nonadiabatic electron acceleration by alow frequency wave [5] is invoked in Sec. 4.
Moreover contribution of laminar electric field pulses
such as electrostatic double layers to the acceleration of highenergy electrons is compared with that of a fairly coherent
lower hybrid wave packet.

We have carried out the high voltage linear discharge
along the magnetic field with a preexisting deuterium plasma
produced by a titanium washer gun [6]. The configuration of
the magnetic field is a magnetic mirror with mirror ratio 1.2
and the field intensity at the mirror point is typically 1.2 kG.
The discharge is ignited by applying a high voltage Vc = 15 –27 kV from a capacitor with C = 2.2 µF between the cathode(aluminum disk 50 mm in diameter) and the cylindricalmuzzle of the plasma gun after a suitable delay time, typically
24 µs from firing the gun.
The parallel electric fields were measured at two axial
positions, one at 10 cm in front of the cathode, and the otherat the centre of the apparatus (midplane), by using a pair ofelectric double probes and optically isolated transmission
systems. The distance of two measuring points is L = 20 cm.
The optically isolated transmission system of the electric field
fluctuations has frequency characteristics whose upper 3 dB
cut-off frequency is nearly 80 MHz.
We have detected hard x-ray fluxes in the direction
perpendicular to the magnetic field line with a plastic
scintillator (NE102A) and photomultiplier combinations
arranged at the centre of the apparatus. The x-ray detector
mounts an aluminium absorber 1-mm in thickness on thedetector head. Hence the energy range of hard x-rays isroughly determined to be larger than 15 keV.

©2004 by The Japan Society of Plasma
Science and Nuclear Fusion Research

Corresponding author’s e-mail: takeda@phys.cst.nihon-u.ac.jp1562

Takeda Y. et al., Electron Acceleration due to Electric Field Bursts Close to the Lower Hybrid Frequency in a High-Voltage Linear Plasma Discharge

plasma discharge was 2.2 × 1012/cm3.
As Fig. 1(b) and 1(c) show, fluctuations in the electricfield are highly enhanced at t = 31.2 µs, the start-up time ofthe plasma discharge, and cause large anomalous resistivity[7].
The hard x-ray emission is coincident with the electricfield bursts and is more intense in the direction perpendicular
to the magnetic field than that in the direction almost parallelto the magnetic field (see Fig. 1(d), 1(e) and 1(f)).
For comparison, we show similar data set in Fig. 2,
which was taken in another discharge shot under the operating
condition VC = 25 kV and Bm = 1.3 kG. Plasma parameters of
the initial plasma were almost the same as the case of Fig. 1.
It should be noted that parallel hard x-ray emissions arecorrelated with electric field bursts shown in Fig. 2(a) and2(b) which broke out nearly 4 µs later than those shown inFig. 1 as the second activity of the electric field, but hard xray emission was not detected in the perpendicular direction.
In order to study this remarkable difference of theangular distribution of hard x-ray emissions, we calculated
power spectral density functions of the electric field bursts
with FFT (Fast Fourier Transform) procedures. Sampled
electric field data are taken from the relevant time interval,
t = 31.0 µs to 33.048 µs for Fig. 1(b) and 1(c), and t =38.0 µs to 40.048 µs for Fig. 2(a) and 2(b). Figure 3(a) and3(b) show notable broadening of the spectral profile aroundthe lower hybrid frequency flh = 55 MHz for a deuterium
plasma in the case of intense hard x-ray emission

We also detected hard x-ray emissions in the forward(cathode side) and backward (anode side) directions almost
parallel to the magnetic field in order to obtain informationon the anisotropy of velocity distribution of energetic
electrons produced in the localized wave structure, such as alower hybrid wave packet.

3. Relationship between electric fieldbursts and hard x-ray emission
Figure 1 shows a typical time profile of the discharge
current flowing in a preexisting deuterium plasma,
fluctuations in the longitudinal electric field, and hard x-ray
emissions detected in the direction both perpendicular andparallel to the magnetic field. This data set wassimultaneously obtained in the same discharge shot, where
the applied voltage between the anode (the muzzle of thetitanium washer gun) and the cathode VC is nearly 27 kV andthe intensity of magnetic field at the mirror point Bm is
1.3 kG. The time sequence of a linear plasma discharge
started at the instant when the titanium washer gun was fired
to produce and inject a deuterium plasma into the magnetic
mirror. The electron density was monitored with a microwave
interferometer which was arranged at the center of theapparatus and operated at the frequency 69 GHz. The meanelectron density before application of the high-voltage linear

Fig. 1

Typical data sets of the high-voltage linear plasma
discharge. The time trace (a) shows discharge current,(b) the parallel electric field E1 measured 10 cm in frontof the cathode, (c) the parallel electric field E2 at thecenter of the apparatus, (d) x-ray emission in thedirection perpendicular to the magnetic field, (e) x-rayemission almost parallel to the magnetic field detectedfrom the cathode side, and (f) x-ray emission almost
parallel to the magnetic field detected from the anodeside.

Fig. 22563

Similar data sets of the high-voltage linear plasma
discharge. The time trace (a) shows the parallel electricfield E1 measured 10 cm in front of the cathode, (b) theparallel electric field E2 at the center of the apparatus,(c) x-ray emission in the direction perpendicular to themagnetic field, (d) x-ray emission almost parallel to themagnetic field detected from the cathode side, and (e)x-ray emission almost parallel to the magnetic field
detected from the anode side.

Takeda Y. et al., Electron Acceleration due to Electric Field Bursts Close to the Lower Hybrid Frequency in a High-Voltage Linear Plasma Discharge

Fig. 3

Power spectral density functions of the electric field fluctuations calculated with FFT procedures. (a) and (b) show the power
spectra using the electric field data shown in Fig. 1, and (c) and (d) are calculated from the electric field data shown in Fig. 2.

t = 27.4 µs are detected only in the direction perpendicular to
the magnetic field. The power spectrum of the electric fieldburst is remarkably more broadened than that in Fig. 3(c).
The physics of preferential electron acceleration
perpendicular to the magnetic field in the case of broadened
power spectrum of electric field bursts is not fully understoodat the present stage, and will be discussed in another paper
referring to the recent theory [5] of electron heating andacceleration due to large amplitude electrostatic waves with afrequency much lower than the electron cyclotron frequency.
Both nonadiabatic motions of electrons perpendicular to themagnetic field and chaos dynamics could be relevant toelectron acceleration and turbulent heating perpendicular to
the magnetic field.
Finally Fig. 5 shows decisive experimental results [9]that a coherent lower hybrid wave packet emerged att = 31.5 µs is coincident with strong hard x-ray bursts and ismore efficient to accelerate high-energy electrons thanpreceding repetitive laminar electric field pulses.
In conclusion, electric field burst with frequency near thelower hybrid frequency is more efficient in electron
acceleration than laminar electric field pulses that represent
coherent structures, such as double layers, if their amplitudes
are comparable.
The presence of counter-streaming electrons is evidenced
by hard x-ray emissions detected from both the cathode andanode sides in the direction almost parallel to the magnetic
field. The simultaneous occurrence of counter-streaming
electrons could not be explained by direct acceleration due todouble layers. The delay time of parallel hard x-ray fluxes
from the electric field pulse, typically 300 ns, also proves thisinterpretation.

perpendicular to the magnetic field. On the contrary, thepower spectrum of the correlated electric field burst isrelatively narrow as shown in Fig. 3(c) and 3(d) in the caseof impulsive hard x-ray emissions preferentially detected in
the direction almost parallel to the magnetic field.

4. Discussion and concluding remarks
In the present experiment, the electron cyclotron
frequency fce is approximately 60 times higher than the lower
hybrid frequency flh = 55 MHz. Since the longitudinal scale
length of a lower hybrid caviton l is estimated to be 5.2 cm
according to the theory of transit time acceleration [4], then
the transit time is ttr = l/ve = 2.8 ns for an electron with kinetic
energy of 1 keV that comprises high-energy tail of theMaxwellian distribution. Then the necessary condition for thetransit time acceleration Tlh = 13.3 ns >> ttr is well satisfied,
where ve denotes the electron velocity and Tlh is the period ofa lower hybrid wave.
Therefore we can assert that the preferential accelerationof energetic electrons parallel to the magnetic field in the caseof fairly monochromatic spectral profile as shown in Fig. 3(c)and 3(d) could be explained according to the theory of transit
time interaction of electrons with a localized lower hybrid
wave packet or an elongated lower hybrid caviton.
Moreover we should mention that the recent theory oflower hybrid turbulence [8] predicts that the electron velocity
distribution has enhanced fluxes of energetic electrons bothparallel and antiparallel to the magnetic field due to nonlinear
wave interaction near the lower hybrid frequency throughmodulational instability, such as the collapse of waves intosoliton turbulence.
Figure 4 shows the opposite case of Fig. 2 and hard xray emissions correlated with the electric field burst around3564

Takeda Y. et al., Electron Acceleration due to Electric Field Bursts Close to the Lower Hybrid Frequency in a High-Voltage Linear Plasma Discharge

Fig. 4The time traces show (a) the parallel electric field E1, (b)x-ray emission in the direction perpendicular to themagnetic field, (c) x-ray emission in the direction
almost parallel to the magnetic field detected from thecathode side, and (d) similar parallel x-ray emission
detected from the anode side. The bottom figure (e) isthe power spectral density function of the electric field
E1 during the period t = 27.4 µs – 28.424 µs.

Fig. 5

References

An electric field burst around t = 27.4 µs is coincident
with intense hard x-ray emissions. The hard x-rayemission is more intense in the direction perpendicular
to the magnetic field than that in the direction parallelto the magnetic field. The time trace (a) shows theelectric field E2 measured at the center of the device, (b)a perpendicular hard x-ray emission at the center, (c) aparallel hard x-ray emission detected from the cathodeside, (d) expanded time trace of the short electric fieldburst shown in (a) during t = 31.4 µs – 31.7 µs. The
bottom figure (e) is the power spectrum of the coherent
wave packet.

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[7] Y. Takeda and H. Inuzuka, Phys. Lett. A 265, 282 (2000).
[8] M. Retterer, Phys. Plasmas 4, 2357 (1997).
[9] Y. Takeda, H. Inuzuka and K. Yamagiwa, Double Layers(World Scientific, 1997) p. 193.

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