New Effects In Physics Of Modern Mirrors
E.P.Kruglyakov, A.V.Burdakov, A.A.Ivanov
Budker Institute of Nuclear Physics, 630090, Novosibirsk, Russia
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Keywords: plasma, magnetic mirrors, beam plasma interaction
PACS: 52.55.-s, 52.55.Jd, 52.50.Gj
One of the crucial problems of plasma confinement in mirrors is longitudinal electron heat conductance. Two
ways of overcoming this problem were demonstrated in our experiments.
In the case of multi mirror trap GOL-3 plasma is heated as a result of interaction of high current relativistic
electron beam (REB) (~1 MeV, 30 kA, 8 μs) with a dense (~1021m-3) plasma. Besides, the experiments have shown
that during the time when the REB was passing through the plasma, very strong suppression (by three orders of
magnitude) of longitudinal electron heat conductance is observed. As a result, the electron temperature of order of 2
keV was obtained in the GOL-3 [1,2].
Both the absolute value of temperature and its inhomogeneous distribution along the device during ~5
microseconds could not be explained under assumption that the plasma energy is lost due to the classical electron
heat conduction. To explain these experimental results, it was assumed in
 that an abnormally high electron-scattering frequency caused by a
strong turbulence occurring in the course of electron-beam injection into
plasma reduces the longitudinal electron heat conductivity by two to
three orders of magnitude, as compared to the classical conductivity (this
problem is considered in more detail in ). Such effects were probably
observed in the experiments on the collective interaction of nanosecond
electron beams with plasma (see, e.g., ); however, due to the short
duration of the process (~50 ns), they did not appreciably alter the
dynamics of beam-heated plasma. Various mechanisms responsible for
anomalous collision frequency in turbulent plasma (see, e.g.,  and
review ) and in the electron-beam systems are known (see, e.g.,
review ). In our case, the following mechanism can be responsible for
this anomaly: during the collective relaxation, the electron beam excites
intense resonance (Langmuir) plasma oscillations. In the case of
nonlinear relaxation of these oscillations, whose level can achieve the
modulation instability threshold, an intense ion sound wave can arise,
together with density modulations associated with Langmuir collapse
processes (a detailed study of turbulent processes accompanying the
relativistic electron-beam relaxation in a magnetized plasma was
performed on a device with different parameters [9, 10]).
Special experiment for direct observation of anomalously low
longitudinal electron heat conductivity was curried out at GOL-3
facility. In the experiments, a short section with a magnetic field of
1.3 T (i.e., 3.7 times lower than in the adjacent regions with a uniform
magnetic field) has been formed in a middle of the solenoid of the GOL-
3 device. Figure 1 show typical waveforms of the plasma pressure derived from diamagnetic measurements. The
initial plasma density in this case was 1021m–3. Far from the cell (at Z= 524 and 701 cm), the signals from
diamagnetic detectors are identical in shape to those observed in experiments without a magnetic well. For
comparison, the figure shows a hard bremsstrahlung signal from a detector located behind the beam collector (this
FIGURE 1. Typical signal of
bremsstrahlung measured behind the
beam collector (W) and the waveforms
of the plasma pressure in the central
plane of the magnetic well (659) and at
two points where the magnetic field is
uniform (524 and 701). The numerals by
the curves indicatethe longitudinal
coordinate Z in cm.
signal provides the most adequate information about the time behavior of the power of the beam passed through the
plasma). In the course of plasma heating by the electron beam, the plasma pressure (which is determined in this
stage by the electron temperature) in the magnetic well is 5–10 times lower than the pressure measured by detectors
located a distance of ~40 cm, where the field is uniform. Due to a decrease in the local electron density of a
relativistic beam in this section, beam-induced plasma heating almost did not occur in the weak-field region. As a
result, a short region with a temperature several times lower than in the surrounding plasma was formed during the
course of beam injection into the initially homogeneous plasma. The measured longitudinal plasma pressure gradient
corresponded to an electron temperature gradient of ~1 keV/40 cm (for the above-mentioned parameters of beaminduced
plasma heating and characteristic time of few microseconds, the ion temperature is much lower than the
electron temperature ). The existence of a low-temperature region is direct evidence of the suppression of
longitudinal electron heat conductivity at the stage of collective beam–plasma interaction and plasma heating.
EFFECT OF FAST ION HEATING AT MULTI-MIRROR TRAP
It is well known that in result of REB – plasma interaction the plasma electrons are heated. Indeed, in the case of
homogeneous magnetic field (with two mirror coils at the ends of solenoid) heating of plasma electrons was
observed. In the case of multi mirror configuration new phenomenon was unexpectedly discovered. In ten
microseconds after switching off the REB ion temperature achieved 2 keV in very short time (~10 microseconds)
and such hot plasma sustained during τE ~ 1 ms .
The mechanism of fast ion heating was studied in the experiments [13,14]. Main points are the following. The
non-uniform electron pressure should produce a longitudinal
ambipolar electric field, which accelerates the plasma on both
sides of the magnetic well toward the central plane of the cell,
where the counter-propagating plasma flows collide. The kinetic
energy of the accelerated plasma ions should depend on the
magnetic field configuration, the total pressure drop, and the
electron temperature profile along the cell.
The mean free path of the accelerated ions in these
experiments is comparable to the cell length or is even longer.
This means that the accelerated ion flows arriving from regions
with a high magnetic field on both sides of the cell should mix in
its central plane because of binary ion–ion collisions and/or
because of the onset of turbulence in counter-propagating flows.
The kinetic energy of the directed ion motion is, therefore,
transformed into their thermal energy.
In the multi-mirror configuration the experiments and
numerical simulations have shown that axially non-uniform
heating of the plasma electrons gives rise to a macroscopic motion
of the plasma along the magnetic field in each mirror cell. The
mixing of the counter-propagating plasma flows inside each cell
leads to fast ion heating. Efficiency of this heating mechanism is
higher than that determined by binary electron–ion collisions.
The mechanism for fast ion heating considered here should
lead to the excitation of large-amplitude waves of the plasma
density. Such density waves were measured directly by Thomson
The plasma motion in the axial direction through the multimirror
system and redistribution of its parameters along the radius
is accompanied by excitation of oscillations inside the hot part of
the plasma column. This is clearly displayed by the signals of
neutron detectors as this diagnostics most sensitive to the plasma parameters (see Fig.2, b). Period of oscillations
agrees well with the predicted period for bounce oscillations. These oscillations make efficient exchange between
populations of slightly trapped and slightly transit ions, therefore the plasma confinements in the multi-mirror
system (which relies on relatively short free path length for ions) improves.
Intensity of neutron emission, a.u.
FIGURE 2. Initial phase of the neutron
emission. There is almost no neutron flux during
initial stage of the plasma heating. Then,
approximately at the moment of emergence of
the large density fluctuations, an intense neutron
flash appears which is followed by a quasi
steady neutron emission up to ~1 ms.
RADIAL PINCH OF FAST ION DENSITY AND HIGH-BETA PLASMA
CONFINEMENT IN AXIALLY SYMMETRIV GAS DYNAMIC TRAP
The gas dynamic trap configuration [15,16] has been proposed as a possible approach to an open-ended
fusion reactor or, as a near-term perspective, as a 14 MeV neutron source [17,18] for fusion materials testing. The
GDT-based reactor would produce power in a long, axially symmetric, high-β, magnetic solenoid. End losses
from the solenoid are reduced by strong increase of the magnetic field at the end mirrors under the condition that
a mirror to mirror length exceeds the ion mean-free path of scattering into a loss cone. In the gas dynamic trap,
the rate at which ions are lost out of the ends is of order of an ion-acoustic speed V Ti . The resulting plasma lifetime
can then be roughly estimated as
τ ≈ R⋅ L , where L is the machine length, and R the mirror ratio15,16. In the
gas dynamic trap, the value of lifetime appropriate for fusion applications can be achieved by increasing both mirror
ratio and the machine length.
More near-term application of the GDT concept is a 14 MeV neutron source for fusion materials
development [17,18]. For this purpose, energetic D and T ions with anisotropic angular distribution are produced in
GDT providing high neutron flux density in localized regions. These energetic ions are provided by angled injection
of ≈ 100 keV deuterium and tritium neutral beams at the center of solenoid. In contrast to the GDT-based reactor,
quite moderate electron temperature of 0.5 ÷ 1 keV is sufficient to generate neutron flux as high as 2 MW/m2. For
given temperature of the warm plasma and energy of the beams, the fast ion angular distribution remains quite
narrow, and centered on the initial value of the pitch angle during their slowing down to considerably lower
energies. This results in formation of sharp fast ion density peaks near the turning points where the ions spend a
sufficiently large fraction of a bounce time. The neutrons are mainly produced in collisions between the fast ions
and, accordingly, the neutron flux density is also strongly
peaked in the same regions that house the testing zones. A
gas dynamic trap has the advantage of confining high-β
plasmas, which produce a higher 14 MeV neutron flux
density (up to 4 MW/m2) that would other plasma based
sources. Numerical simulations indicate that neutron flux
density approaching 4 MW/m2 could be generated in the
testing zones This property of GDT is vital to the high
performance of the source and, therefore, should be
experimentally proven. Note that for a magnetic mirror
with quadruple min-B field, MHD stable confinement of
a plasma with β ≥ 1 has been already demonstrated .
The experiments supporting the GDT–based neutron
source development are carried out at GDT device in
Novosibirsk. The magnet and neutral beam systems of the
device are shown in Fig. 1. The vacuum chamber consists
of a cylindrical central cell 7 m long and 1 m in diameter
and two expander tanks attached to the central cell at both
ends. A set of coils mounted on the vacuum chambers
produce axially symmetric magnetic field with a variable
mirror ratio ranging from 12.5 to 75 when the central
magnetic field is set to 0.28 T.
The finite-β plasma in central solenoid is stable against magnetohydrodynamic instabilities because along a
magnetic field line the minimum-B axially symmetric end cells provide a favorable pressure-weighted curvature. To
ensure this stability, a sufficiently high density plasma is maintained in the end cells by collisional losses of the
warm plasma from central solenoid .
The initial plasma is produced by a ≈ 3 ms pulse from a washer stack hydrogen-fed plasma gun. located in
one of the end tank beyond the mirror throat. Subsequently, the plasma was heated and fast ions were produced by 6
deuterium neutral beams. The deuterium beams are used instead of the hydrogen ones, which are routinely injected,
in order to slightly increase the beam trapped fraction and obtain additional diagnostic capabilities. Neutral beam
currents in excess of 250 equivalent atomic amperes were injected with an accelerating voltage 15-17 keV. The
beam duration of each injector is set to 1 ms. About 2.6 MW have been trapped by the solenoid plasmas.
FIGURE 3. Radial profile of magnetic field
perturbation and plasma density (circles).
Plasma heating and fast ion density buildup caused increase of plasma diamagnetism. The measured radial
profile of the ΔB B mapped on to mid-plane is shown in Fig. 2 together with plasma density profile .
According to the data presented in Fig. 3, the magnetic field perturbation amounts to ≥ 0.2 on plasma axis. It
allows to conclude that perpendicular plasma β exceeds 0.4. The distinctive feature of the radial profile is its quite
small width. It amounts to about 7 cm at 1/e level mapped onto the GDT mid-plane. This is only slightly larger than
the fast deuteron gyroradius ( cm i ρ ≈ 5.6 ) calculated for the magnetic field of 0.25 T and for 10 keV energy that is
close to the fast ion mean energy. One could expect significantly wider profile of the fast ion density taking into
account that the target plasma radius is ~15cm. However, it was observed that fast ion density profile is about two
times narrower indicating presence of a mechanism of fast ion radial pinching. This mechanism is now under study.
The plasma parameters, the most important of which is electron temperature, in the GDT experiment are at present
quite far from needed to produce required 2 MW/m2 of 14 MeV neutrons with D-T plasmas. Therefore, a
modernization of the GDT is being realized. Six new ion sources were constructed providing higher power (10 MW
instead of 4) and longer duration (5 ms instead of 1) of the neutral beams. According to calculations, with the
upgraded neutral beams the plasma parameters in the GDT device would reach those required to produce neutron
flux density of 0.5 MW/m2 in the neutron source thus demonstrating its feasibility from physical viewpoint.
Although the neutron flux for full scale (2 MW/m2 ) neutron source for materials testing should be still four times
higher, at present, even such moderate NS could be already used in variety of applications. Besides, if these
parameters are achieved, those for full scale NS could be predicted with good reliability.
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