Formation of Electron Vortices in Ion Beam Plasma in Crossed E×B Fields
Yu. Chekh, A. Goncharov, I. Protsenko, A. Evsyukov
Institute of Physics National Academy of Sciences of Ukraine,
46, pr. Nauky, Kyiv, 03028, Ukraine
Abstract. The nonuniform density distribution of magnetized electrons compensating the beam of positively charged ions
in crossed ExB fields results in the excitation of strong beam-drift instability which amplifies the electrostatic waves
propagating in ExB direction. We investigate experimentally the nonlinear stage of instability development, where the
waves can trap electrons creating the vortex chain. With the use of wide aperture (∅ 7.4 cm) electrostatic plasma lens we
fix the annular electron density distribution (with the density up to 1.5⋅109 cm-3) in medium-energy (< 40 keV) highcurrent
(0.4 A) heavy-ion (Cu) beam, thus creating the condition for anharmonic large-amplitude (up to 1 kV) lowfrequency
electrostatic waves to be excited. By measurements of the electric field distribution in the lens central plane,
we establish that electron bunches (arising due to instability) contain trapped electrons rotating around the corresponding
bunch with high velocity, in such a way making up the vortex. The velocities of electrons trapped in each separate vortex
of the chain are found to be sufficiently higher than that of the vortex movement as a whole around the lens axis. The
main mechanism of the stabilization of vortex amplitude is established. Considered vortex structures are nonneutral that
defines high electric fields realized within them.
Keywords: vortex-chain, beam-drift instability, ion beam plasma, nonneutral plasma, electrostatic plasma lens, electron
PACS: 52.25.Xz, 52.35.Fp, 52.35.Kt, 52.35.Mw, 52.35.Qz, 52.27.Jt, 52.35.We.
In the theory of plasma physics, plasma is often assumed to be quasineutral. The deviation from this rule is
possible for beam plasmas , diode plasma systems [1, 2], various plasma-optical devices [3, 4], plasmas with
high-frequency electromagnetic oscillations, and obviously in one-component plasmas . Recent researches of
tokamak plasma also reveal fact that the assumption of quasineutrality does not allow to analyze all the variety of
tokamak operation regimes correctly [6, 7]. We investigated the possibility for nonneutral vortices to be formed in
two-component low-temperature collisionless ion beam plasma consisting of positive unmagnetized ions of
medium-energy beam and magnetized electrons. Such a medium can be formed in the electrostatic plasma lens [3,
8]. This lens is an axially symmetric plasma-optical device intended for positive ion beam manipulation. In fact, it is
an electron trap, where electrons are retained in longitudinal and radial directions by the electrostatic and
magnetostatic fields, respectively. Electrons are generated by the peripheral ions through the ion-electron emission
from electrodes of the lens, some part of these electrons remains in the lens providing equipotentialization of
magnetic field lines [3, 4]. In the used experimental conditions magnetic field is strong enough to magnetize
electrons, but practically has no effect on the ions. Similarly, the voltage applied to the lens electrodes is sufficiently
high to realize overthermal space-charge electric field but it is still small for ion trajectories to be effectively bended.
The electric field of the negative space charge in the lens and externally applied magnetic field result in the
azimuthal drift of electrons with velocity
V = [E × B]/B2, (1)
where E is the electric field intensity, B is the magnetic field induction. It is known that the radial gradient of the
drift velocity (or shear) causes the excitation of strong instability [9-11]. This gradient may arise due to the presence
of radial magnetic field gradient or nonuniform distribution of electron density. The excitation of instability results
in the bunching of electrons and their self-consistent electric fields cause additional vorticity of electron trajectories.
As it was shown theoretically [10, 11], these bunches, having approached some density, can create the chain of
electron vortices with closed trajectories of electrons. In this paper we present the experimental results of
investigations of nonlinear stage of instability at the large radial gradient of electron density.
EXPERIMENTAL SETUP AND APPROACH
The experimental setup is shown in Fig. 1. A vacuum arc ion source  with a grid anode and three-electrode,
multi-aperture, accel-decel ion extraction system was used. The extractor contains 84 individual beamlet holes of
4 mm diameter, spanning an overall diameter of 55 mm. Ion beamlets extracted from emission holes widen during
propagation in the space between source and lens to form practically uniform ion beam current density at the lens
inlet aperture. The source operates in a repetitively-pulsed mode and produces moderate-energy, broad, heavy metal
ion beam with principal parameters for the work described here: beam pulse duration – 100 μs, pulse repetition rate
0.5 pps, beam extraction voltage – 12 kV, beam current Ib = 400 mA, Cu ion species.
The electrostatic plasma lens (Fig. 2) had an input aperture diameter of 7.4 cm and a length of 16 cm. The
maximum positive DC potential ϕL = 1 kV was applied to the central lens electrode and several symmetrically
arranged adjacent pair electrodes, the other electrodes being grounded. Most experiments were performed at high
voltage applied to the central electrode and one pair of adjacent electrodes (conditionally denoted as Short Potential
Distribution (SPD)). The magnetic field with the induction of 40 mT at the PL center was created by permanent
magnets. The vacuum chamber pressure was ≤ 1.5 × 10-5 Torr, allowing plasma formation within the lens volume by
the beam itself via ion-electron emission from the lens electrodes.
FIGURE 1. Scheme of experimental setup;
1 – vacuum chamber; 2 – ion source;
3 – capacitive or Langmuir probes;
4 – plasma lens; 5 – ion beam; 6 – collector.
FIGURE 2. Plasma lens; 1 – permanent magnets; 2 –
magnetic conductor; 3 – magnetic field lines; 4 –
The azimuthal and radial distributions of electrostatic potential were studied using a system of capacitive probes.
The azimuthal profile of the wave potential was derived from the voltage time series measured by the probes. The
azimuthal wave velocity was calculated from a time shift of the phase of oscillations detected by two probes spaced
by a definite azimuthal angle. The radial electric wave field was measured by a pair of double capacitive probes
spaced by 5 mm, each probe sensor having a diameter of 1 mm and length of 5 mm. The measuring circuits had
equal (within the limits of ~ 10 %) transmission coefficients in a frequency band from 100 kHz to 15 MHz. The
distributions of potential could not be adequately determined on a time scale of the beam pulse duration due to some
factors of the circuits, therefore the constant (within ≈ 20 μs) potential component in the PL was determined using a
single Langmuir probe that could be moved in the radial direction. The constant potential component was measured
in the time interval between electron bunches. In these intervals the plasma medium is least perturbed by the fields
of electron bunches. For this reason, we denote the potential distribution and corresponding electric field distribution
measured by the Langmuir probe as “background”. All probes were introduced nearly parallel to the system axis,
their sensitive tips being placed in the central cross section of the PL. The signals were measured using an S8-14
oscillograph with a working bandwidth of 50 MHz.
We used high voltage applied to the neighboring electrodes for annular electron density distribution to be
created. Electrons emitted from the lens electrodes have to make magnetic field lines to be equipotential, following
to the externally applied step-like potential distribution over the electrode system. In turn, the step-like radial
potential distribution corresponds to the mentioned above annular electron density distribution. This method enables
to localize the region of instability excitation, as well as to manipulate its spatial position.
As it was anticipated, the maximum amplitude of the waves was observed in the range of localization of the
potential step (Fig. 3). The observed large amplitude anharmonic waves (Fig. 4) were found
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