Laboratory Modeling and Artificial Stimulation of the Magnetospheric Maser Effects

A. S. Belov, Yu. V. Chugunov,* G. A. Markov, and L. L. Popova
Department of Radiophysics, University of Nizhny Novgorod
23 Gagarin Ave., Nizhny Novgorod 603950, Russia
* Institute of Applied Physics, Russian Academy of Sciences
46 Ul’yanov Str., Nizhny Novgorod 603950, Russia
Abstract. We develop a method for creation of a magnetospheric plasma resonator formed a by high-frequency whistler
range discharge in the linear mirror magnetic system. We discuss the results of laboratory modeling and artificial
stimulation of the maser effects in the Earth’s magnetosphere at the bounce frequencies of oscillations of the fast electron
beams between the magnetic mirrors.
Keywords: Laboratory studies of space- and astrophysical-plasma processes, high-frequency and RF discharges.
PACS: 52.72.+v, 52.80.Pi.
Generation of ELF emission in the Earth’s magnetosphere is usually related to the resonant interaction of whistler
and Alfvén waves with the charged particles of the radiation belts. For example, we can point out the maser effects
caused by the development of the cyclotron instability in the magnetospheric resonator formed by a density duct and
ionospheric mirrors, excitation of the Pc pulsations under the magnetic-field reconnection in the magnetosphere tail,
trigger effects, etc.
A possibility of klystron instability in the resonator placed in the returning electric field exists. For example,
electrons oscillate with the frequency ω = 2α e m in the parabolic potential well 2
0 0 ϕ(z) =ϕ −α (z − z )
( e and m are the charge and mass of electron, respectively, ( ) 0 z − z is distance from the center of the well, and
α is a constant). In the Earth’s magnetosphere there is also a possibility of generation of electromagnetic
disturbances stimulated by the longitudinal oscillations of the energetic electrons moving without collisions between
the conjugated magnetic mirrors in the magnetospheric resonator. In [1], modulation of the chorus emissions in the
auroral magnetosphere is explained by the bunching of bounce electrons in the field of magnetohydrodynamic
High cost of space experiments and the technological difficulties of realization of the synchronous measurements
of the energy spectra of charged particles and wave processes at the different end of the disturbed magnetospheric
flux tube make it extremely difficult to verify experimentally the theoretical studies in the natural conditions.
The experimental setup is shown in Fig. 1. The magnetic field was produced by two solenoids (coils 1 and 2)
with independent power supplies. This allowed us to vary the longitudinal profile of the magnetic induction B (z) z
from quasi-uniform to that corresponding to a magnetic-mirror configuration. A steady-state plasma column was
produced by a plasma-wave RF discharge in the whistler frequency range LH He ω ≤ω ≤ω , where LH ω is the
lower hybrid resonance frequency, He ω is the electron gyrofrequency, and ω is the radiation frequency. The
discharge was excited in a 150 cm long, 6 cm diameter glass tube under conditions of the ionization self-ducting of
waves excited in the above frequency range by a quadrupole antenna consisting of three copper rings placed around
the tube in its central part at a distance of 6 cm from one another. The RF voltage ( 0 f =200 MHz, 0 V =50 V) was
applied to the exciting rings from a GST-2 oscillator through a coaxial cable. The central conductor of the cable was
connected to the central ring, whereas the outer conductor of the cable was connected to the side rings. The working
gas was air. The input RF power was about 10 W. The plasma density averaged over the cross section of the
discharge column N = ∫ N f x dx R⊥

0was measured by a microwave interferometer operating at a frequency
of 9.5 GHz. Here, ( ) 0 N f x is the distribution of the plasma density,
effective radius of the plasma column.

A distinctive feature of the ionization self-ducting of waves in the whistler frequency range in a nonuniform
magnetic field is the narrowing of the plasma column and a substantial increase in the plasma density in the region
where the field B (z) z is strong. It should be noted that the profiles B (z) z , N (z) e , and R⊥ (z) are similar to the
longitudinal profiles of these quantities in a magnetospheric duct with enhanced plasma density and are typical of
natural magnetospheric resonators in the whistler and Alfvén frequency ranges. This allows us to use the laboratory
resonator to model resonant and nonstationary wave phenomena occurring in the Earth’s magnetospheric resonators.
Nonequilibrium state of the plasma in the laboratory model is provided for the hot part of discharge electrons
trapped in the mirror magnetic system because of the large transverse velocities.
Stationary distribution of the electric potential along the longitudinal axis z respective to the distribution of the
plasma density N (z) e is the potential well for electrons. At low pressures in the discharge tube ( P <10-4 torr), it is
possible to observe the entire spectrum of electromagnetic instabilities in this resonator [2]. The spectrum of lowfrequency
radiation generated by a plasma-wave discharge comprises three groups of fairly narrow lines, which can
be attributed to the ion-cyclotron resonances of the main (singly, doubly, and triply charged) plasma ions. Moreover,
one can see rather wide maxima associated with the generation of magnetoacoustic (MA) and ion-acoustic (IA)
waves by the plasma wave exciting the discharge in the central region of the magnetic confinement system. As the
pressure increases up to P ~10-4 torr, the ion-cyclotron lines disappear, but the lines associated with the generation
of ion-acoustic waves disappear only at P ~6·10-3 torr. After switch-off of the magnetic field in the magnetic-mirror
region, the ion-cyclotron lines cease to be generated.
Furthermore, it is possible to observe the generation of electric–field oscillations at the bounce frequency of the
longitudinal oscillations of discharge electrons with energy E ~260 eV ( 1 f ~4.15 MHz). The power spectral density
of the electric field oscillations in this resonator is shown in Fig. 3. It is important that the position of the generated
peak is almost independent of the magnetic field strength at the center of the mirror magnetic confinement system
and the magnetic mirror ratio. The energy of bounce electrons that can excite the longitudinal oscillations at
frequency 1 f must be sufficiently large. Our discharge contains these electrons, because the positive potential of the
plasma column is sufficiently large at low pressures in the discharge tube ( P <10-4 torr, ϕ >600 V). However, the
number density of these electrons is small, so that the sensitivity of a multigrid energy analyzer is insufficient for
their registration. In this case, the excitation of the generated peak is possible only in the presence of the propagating
high-Q mode at this frequency. Resonant wave fields provide the feedback for effective grouping of fast electrons
and resonance amplification of the exciting oscillations.

FIGURE 4. Fragment of the experimental dependence of the fast-electron flux I (t) e on the flight time t for altitude
h >140 km.
Moreover, one can see several time intervals, namely, 2 τ ~2 s, which is the period of bounce oscillations of fast
electrons (40 keV) between the poles of different hemispheres, 3 τ ~0.3 s, which is the period of oscillations of
ionospheric Alfvén resonator, and 4 τ ~1 s, which is the relaxation or transient time of the electron flux under switchon
and switch-off of the pump generator. It should also be noted that the power of the generator is insufficient for
acceleration of the particles with this energy (>40 keV). Therefore, we can state that the observed oscillations are the
longitudinal oscillations of fast electrons from the radiation belts in the magnetospheric resonator. The resonator was
formed by the density duct and potential barriers for particles at the conjugate regions of the auroral ionosphere. The
dispersion characteristics of the magnetospheric plasma of the L-shell allow the excitation of the
magnetohydrodynamic perturbations with different spatial scales by the bounce oscillations. As a result of this
interaction, it is possible to increase noise ELF emission [4].
In conclusion, the experimental results allow us to say about necessity to account fot  
excitation of ELF emission. An important result is a possibility of stimulating these perturbations by radio-frequency
discharge in the Earth’s ionosphere, shown in the laboratory and ionospheric experiments. Controlled perturbations
of this type may particularly be important for active diagnostics of the magnetosphere tail.
This work was supported by the Russian Foundation for Basic Research (project No. 04–0216506a) and the
Russian program “Leading Scientific Schools” (project No. NSh–6043.2006.2).
1. P. A. Bespalov, S. A. Grach, and V. Yu. Trakhtenhertz , Sov. J. Plasma Phys. 3, 1050-1060 (1977).
2. Yu. V. Chugunov, V. V. Dobrokhotov, N. M. Lukshin, and G. A. Markov, Plasma Phys. Rep. 85, 2503-2504 (2005).
3. Yu. V. Chugunov and G. A. Markov, J. Atmos. Sol.-Terr. Phys. 63, 1775-1787 (2001).
4. Yu. N. Agafonov, V. S. Bazhanov, Yu. I. Gal’perin et al., Sov. Tech. Phys. Letters 16, 627-631 (1990).

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