Phenomenon of Anomalous Fast Heating of Ions during Relaxation of Electron Beam in Plasma of Multimirror Trap GOL-3

V.T. Astrelin, A.V. Arzhannikov, A.V. Burdakov, G.E. Derevjankin, I.A. Ivanov,
M.V. Ivantsivsky, K.I. Mekler, S.V. Polosatkin, V.V. Postupaev, A.F. Rovenskikh,
S.L. Sinitsky, J.S. Suliaev, Yu.A. Trunev, A.A. Shoshin and E.R. Zubairov
Budker Institute of Nuclear Physics, Novosibirsk 630090, Russia
Abstract. Phenomenon of fast heating of plasma ions in the GOL-3 facility being operated in multimirror mode is discovered
and explained. An essence of effect is that ion component of the plasma is heated during high-current electron beam injection
much faster (at 100-1000 times) than in the case of classical transfer of energy from electrons to ions due to binary collisions.
This method allowed us to heat plasma up to temperature 2 keV at density of (0.5-1) 1021 m-3.
The phenomenon of fast ion heating is investigated experimentally and theoretically. A model of fast non-Coulomb
ion heating was suggested for explanation of this effect. Results of investigation are presented in the report.
Keywords: Beam-plasma interaction, multimirror magnetic system, plasma heating, collective acceleration of ions,
numerical simulation.
PACS: 52.55.Jd; 52.50.Gj
An investigation of plasma heating and confinement in a long open magnetic trap is carried out at the GOL-3
facility [1] in Budker Institute of Nuclear Physics. The facility consists of multimirror trap with corrugated magnetic
field and generator of high-current relativistic electron beam being used for heating of dense deuterium plasma np ~
1021 m-3 placed in the trap. The multimirror configuration of magnetic field essentially increases the plasma energy
lifetime. It occurs due to collisional friction between transiting and trapped ions and it is effective if a mean free path
of ions is between the length of one magnetic cell and total length of trap [2].
A strong beam-plasma interaction and subsequent turbulence lead to effective heating of plasma electrons [3]. In
earlier experiments in the magnetic trap with uniform (non-corrugated) magnetic field in the solenoid a temperature
of plasma electrons was raised up to Te ~ 1-2 keV due to collective processes at the turbulence. This result became
possible thanks to a strong suppression of electron thermal conductivity along the magnetic field observed in
turbulent plasma. An ion temperature does not exceed Ti ~ 50 eV during and after the electron beam pulse. An
electron temperature decreases to level of ~ 100 eV at ~ 30 μs after the beam pulse.
A situation has changed strongly after transition to multimirror regime of plasma heating and confinement. The
heating of electrons remains practically the same (Te ~ 2-3 keV for a beam of higher density of current). As for ion
energy, it increased up to value of order of keV after beam pulse of τb ~ 6-8 μs duration. A hundred microseconds
later the ion temperature becomes Ti ~ 1-2 keV although the electron temperature decreases to ~ 100 eV [3]. This
fast transfer of energy from electrons to ions can not be explained by classical binary e-i collisions for given plasma
density, because the classical energy exchange time (τclass ~ 4 ms) is much greater than observed in the experiment
(τexp ≤ 10 μs).
The paper consists of review and analysis of experimental facts that prove an anomalous character of ion heating
in the multiple mirror trap GOL-3. It considers some estimates and a model.

Scheme and Parameters of the Experiment
The scheme of the GOL-3 facility and magnetic field
distribution on axis are shown on Fig.1. A length of
solenoid is L ~ 12.4 m, it consists of N = 55 magnetic
cells of a length l = 22 cm with magnetic field Bmax/Bmin =
4.8/3.2 T placed between end mirrors of B ~ 9 T. A
vacuum chamber placed inside the solenoid is a metallic
tube, being filled with deuterium through fast puffing
valves. A linear electric discharge in the gas produces
plasma of density np ~ 1020
– 1022
m-3. The initial gas
density is almost constant inside interval 1 – 11 m and
falls at an order to edge mirrors. A relativistic electron
beam passes a plasma column and dumps to a collector
placed in a magnetic field of 0.1 T at 1 m distance after
the output mirror. Peak parameters of the beam are: an
energy eUb ~ 1 MeV, a current Ib ~ 25 kA and duration
of pulse is τb ~ 8 μs. A total energy content of the
electron beam is Wb ~ 120 kJ. Pitch-angles of electron
velocities in corrugated magnetic field are calculated as
≤ 0.2 rad. So as electrons of the beam are magnetized in
their motion, a density of beam electrons is proportional to magnetic field and changes along the trap approximately
as nb ~ (2-3)·1017 m-3.
Particular Features of Plasma Electrons Heating
Some particular features of this process had been found during the experimental investigations of beam-plasma
interaction. The main are the following. 1) The interaction develops if increment of beam-plasma instability exceeds
an electron collision frequency. This approximately corresponds to condition nb/np > 10-4 for parameters of beam and
plasma used in GOL-3 that was shown experimentally [3]. For multimirror experiment described above this
condition means that development of turbulence and electron heating will occur only in maxims of corrugated
magnetic field, where ratio nb/np is maximal. In minims of the field the increment of plasma instability becomes less
than electron collision frequency and heating of electrons doesn’t take place. 2) A developed beam-plasma
turbulence suppresses an electron thermal conductivity and recovers it after the end of the beam pulse.
To prove this, the following experiment has been performed [4]. In a section of solenoid with uniform magnetic
field 4.8 T a special cell with a reduced magnetic field 1.3 T and a length 0.5 m was formed. As measurements
show, during the beam pulse (tb ~ 5 μs for this experiment) the plasma pressure in the magnetic well is much less (in
~5-10 times) than outside. This may be explained only by factors 1) and 2) acting simultaneously because initial
space distribution of plasma density is almost uniform. The plasma pressure gradient corresponds to electron
temperature gradient up to 2.5 keV/m.
After the beam pulse the plasma pressure falls everywhere except the region of the magnetic well where rest
plasma energy is greater than outside. So as the electron temperature evens out along the system due to recovered
electron thermal conductivity it may be a result of a local increasing of plasma density or/and ions energy.
Evidences of Fast Ions Heating in Multimirror Regime
• Results of experiments show that in multiple mirror regimes an intensive ion heating occurs. It follows from
measurements of ion temperature by a Doppler broadening of Dα-line. Its dynamics is shown in Fig.2.
• The fact of sufficient heating of ions is confirmed by time dependence of diamagnetic pressure in the plasma
column (Fig.3). So as electron temperature and electron pressure falls down an order during ~ 30 μs after the

beam pulse, almost all the rest pressure belongs to ions. Such a way, an ion energy rising time is close to beam
duration. In this experiment with higher plasma density an ion temperature of Ti,max ~ 1 keV is received.
• Then, registration of charge exchange neutral atoms from the plasma and analyses of their energy distribution
shows that they appear at once with beam pulse and may be described by temperature Ti = 1.5 ±0.5 keV (Fig.4).
• At last, it was found that heated plasma radiates neutrons. A time dependence of neutron flow shows (Fig.5) that
neutron emission begins after a beam pulse, rises slightly during ~ 100 ms (ions thermal equilibration time) and
then slowly falls down with decay time ~ 0.5-1 ms. A total flow of neutron emission from the plasma
corresponds to temperature of ions Ti ~ 1 keV.
An average time of ions heating due to electron-ion classical Coulomb collisions is τei ~ 4 ms for plasma density
np ~ 1021 m-3 and electron temperature Te ~ 2 keV. So, we may insist that we have a phenomenon of ion heating up
to almost electron temperature during time much less than classical e-i collision time. Below we consider the
physical model that explains transfer of electron thermal energy to ions due to collective process of ions acceleration
under electron pressure.
A Model of Fast Collective Acceleration of Ions
Above written features of plasma electron heat transfer and results of the experiment with the magnetic well
show evidently the following sequence of plasma processes. The interaction of the electron beam with the plasma of
homogeneous density in corrugated magnetic field results in heating of plasma electrons in phases of maximal
magnetic field. Electron temperature is not smoothed along the system due to suppression of electron heat

amplitude, V
Heating by electron beam
Confinement time
Time, ms
Deuterium density
1.9⋅10 21 m-3
«establishment time»
FIGURE 5. Emission of DD-neutrons from plasma.
conductivity by turbulent electric fields. As a result, high gradients of electron pressure appear that accelerate
plasma layers toward areas of minimal pressure. This process is similar to motion of plasma in ion sound wave. So,
we can estimate energy of ions using linear approximation for a wave, as Wi,max ~ MCs
2(ñ/np)2/2 ~ Te/2 for high
amplitude perturbations ñ ~ np. Here Cs
2 = Te/M is a phase velocity of ion sound wave. But so as a front of wave
moves to region with small temperature, it may be similar to supersonic wave. Further, we may use another extreme
estimate as for expansion of dense plasma to vacuum [5]. Here after collision of two opposite flows their
temperature would be close to T = 3/2 Te.
The most important result of these estimates is that energy of ions depends on electron temperature and differs
from it with a coefficient of the order of unity. The mechanism of this phenomenon is a collective acceleration of
ions under the electron pressure gradient. Duration of the process is a time of ions motion at a half of magnetic cell
length. For considered experiments (Wi ~ 1 keV and l/2 = 11 cm) a time of ion acceleration would be of order a
Numerical Simulation of Ions Acceleration in
Multimirror Trap
A hydrodynamic one-dimensional one-fluid two-temperature code
was used for a numerical simulation of plasma dynamic in corrugated
magnetic field under heating by an electron beam [6]. The code
includes particular features of electron heating, observed in the
experiment. It allows simulating of plasma dynamics until collision.
Results of modeling are presented on Fig.6 where characteristics of
plasma in a real magnetic field are shown at some instants. Collisions
of opposite moving flows take place at t ~ 1.6-2 μs. As follows from it,
for t = 0-1 μs ion velocities increase together with electron temperature
and reach to Wi ~ 100-140 eV for Te ~ 400-800 eV. This result
qualitatively confirms with experiments. Note, that after collision of
waves their longitudinal kinetic energy transfers to thermal motion. As
Fig.3 shows, maximal transversal plasma pressure is reached at t ~
120 μs, which corresponds to ion-ion collision time tii ~ 100 μs.
Another important result of modeling is a predicting of a high level
of density perturbations ñ/np ~ 0.5 – 1. A similar perturbations with
amplitude ñ/np ~ 0.4 were observed in the experiment [1] after the end
of beam pulse.
In such a way, the described phenomenon of fast ion heating may be explained as a result of collective
acceleration under electron pressure gradient with subsequent thermalization. Thanks to multimirror configuration of
magnetic field GOL-3 and some specific features of electron heating in a beam-plasma system it becomes possible
to heat ions up to almost electron temperature. These circumstances make possible, in principle, to consider
multimirror trap with electron beam heating as a basis for the following development toward fusion parameters.
The work was partially supported by grants RFBR 03-02-16271 and RFBR 04-01-00244.
1. V.V.Postupaev et al., 12th ICPP, Book of Abstracts, 2004, p.277;
2. A.J Lichtenberg, V.V Mirnov, “Multiple Mirror Plasma Confinement”, in: Reviews of Plasma Physics, 19 (Kadomtsev, B.B.,
Ed.), Consultant Bureau/Plenum Press, New York, 53 (1996).
3. V.S. Koidan., et al., Transactions of Fusion Technology, 47, No.1T, 35 (2005).
4. A.V.Arzhannikov et al., Plasma Physics Reports, 31, 462 (2005).
5. D.D.Ryutov, “Gas dynamics of dense plasma clouds in solenoid”, Preprint INP 90-143, Novosibirsk (1990) (In Russian).
6. V.T.Astrelin et al., 30th EPS Conference

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