1063-7850, Technical Physics Letters, 2006, Vol. 32, No. 1, pp. 51–54. © Pleiades Publishing, Inc., 2006. Original Russian Text © Yu.N. Chekh, A.A. Goncharov, I.M. Protsenko, 2006, published in Pis’ma v Zhurnal Tekhnicheskoœ Fiziki, 2006, Vol. 32, No. 2, pp. 8–14.

Large-Scale Electron Vortex Structure Formation in a Plasma Lens Yu. N. Chekh*, A. A. Goncharov, and I. M. Protsenko Institute of Physics, National Academy of Sciences of Ukraine, Kiev, Ukraine * e-mail: [email protected] Received August 22, 2005

Abstract—The first experimental data on the observation of electron vortices in an electrostatic plasma lens at a considerable radial gradient of electron density are reported. It is established that anharmonic potential waves of large amplitude appear and propagate in the azimuthal direction. The results of measurements of the electric field distribution show that electron bunches formed as a result of instability development contain trapped particles, which rotate at a large velocity around the centers of bunches, thus creating vortices. The main factor leading to limitation of the maximum amplitude of vortices in a strong magnetic field has been experimentally established. PACS numbers: 52.35.Qz DOI: 10.1134/S1063785006010172

Electrostatic plasma lens (PL) is a device intended for the focusing of high-current beams of positive ions. The PL operation is based upon the principles of plasma optics originally formulated by Morozov [1]. The medium for a PL is formed by the propagating intense ion beam and by electrons appearing due to the ion-induced secondary emission. The PL represents an axisymmetric electromagnetostatic trap in which electrons are retained by the electric field in the axial direction, and by the magnetic field in the radial direction. It is the negative space charge accumulated in the PL that ensures the focusing of ions.

ary states in an azimuthally homogeneous PL. It was shown that a layer distribution of electron density could be created. Owing to the principle of equipotentialization, such electron layers concentrate at the field lines that pass via the gaps between cylindrical electrodes, thus ensuring the transfer of a stepwise potential distribution along the electrode system into the PL volume. The greater the potential difference between the neighboring electrodes, the higher the electron density in a layer. This Letter reports on the formation of a single dense electron layer by means of the creation of a potential distribution with one large “step” between electrodes. It is shown that the excitation of largeamplitude oscillations is possible in this electron layer.

As is known, the slippage of electron layers in the ion beam plasma, which occurs in crossed electric and magnetic fields, leads to the development of a low-frequency beam drift instability [2]. This slippage can be induced both by the magnetic field gradient and by the electron density gradient. In the PL geometry, this instability results in the excitation of large-amplitude potential waves propagating in the azimuthal direction [3].

The experiments were performed in a setup that was recently described in detail elsewhere [8]. We used a pulsed periodic beam of copper ions (pulse duration, 100 µs; repetition rate, 1 Hz; current amplitude, 400 mA) with a wide aperture (initial diameter, ~6 cm) extracted at an accelerating voltage of 12 kV from a vacuum-arc ion source [9]. The PL was created between cylindrical electrodes (denoted PLk in [8]) with a radius of 37 mm. The isolating magnetic field was generated by permanent magnets, with a magnetic induction of 40 mT at the PL center. The maximum positive potential ϕL = 1 kV was applied to the central electrode and several symmetrically arranged adjacent pair electrodes; the other electrodes being grounded. Most experiments were performed using the central electrode and one pair of adjacent electrodes (SPD configuration). The residual gas pressure was maintained on a level not exceeding 1.5 × 10–5 Torr.

When the wave amplitude reaches a certain level, the wave field can trap electrons. Since any deviation from quasi-neutrality in a magnetized plasma gives rise to vorticity in the electron velocity field (see, e.g., [4, 5]), the onset of electron trapping can result in the formation of a vortex or a chain of vortices, depending on the number of initial electron bunches created as a result of the development of instability in the linear stage. Here, by vortex is implied a localized structure with current lines closed inside a certain separatrix surface (cf. [6]). Previously, two-dimensional numerical simulation [7] under the conditions of maximum approach to experiment was used to study the formation of station51

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(c)

(f)

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(e) Fig. 1. Oscillograms of the potential oscillations in the PL central cross section, as measured using the capacitive probes at r = 5 (a), 20 (b), 27.5 (c, f), 30 (d), and 32.5 mm (f) (SPD configuration, ϕL = 1 kV, mθ = 5). Sweep: 140 D/div (vertical); 0.5 µs/div (horizontal), except for (f) 0.002 µs/div.

The azimuthal and radial potential and field distributions were studied using a system of capacitive probes. The azimuthal profile of the wave potential was determined 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 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 a length of 5 mm. The measuring circuits had equal transmission coefficients accurate to within ~10% in a frequency band from 100 kHz to 15 MHz. The circuit characteristics were such that the potential could not be adequately determined on a time scale of the beam pulse duration. For this reason, 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 without integration of the current collected in the time interval between electron bunches (which determined the observed waves). In these intervals, the plasma medium is least perturbed by the fields of electron bunches. For this reason, the potential distribution and the corresponding electric field distribution determined by the Langmuir probe will be referred to as the background.

All probes were introduced parallel to the system axis and arranged so that their sensors occurred in the central cross section of the PL. The signals were measured using an S8-14 oscillograph with a working bandwidth of 50 MHz. The results of measurements, which were performed at a significant potential difference applied to the neighboring electrodes and in a rather broad range of conditions in the PL volume, showed that regular anharmonic waves of large amplitude ~ϕL (Fig. 1) appear and propagate in the E × B drift direction (E is the background electric field). The frequency of rotation ν) of the constant-phase regions around the PL axis, as well as the number of wavelengths (mθ) within 360° azimuthal angle interval depend on the distance of a potential step (created by electrodes) from the axis and on the magnitude of this potential jump. For the same electrode potential ϕL = 1 kV, the frequency ν varied within 200–500 kHz and the mθ value varied within 4–6, depending on the particular potential distribution. The observed nonlinear waves exhibited maximum amplitude in the region of localization of the potential step (Fig. 2). The possibility of particle trapping by the wave field (in other words, by the field of electron bunches) is determined by the magnitude of radial electric fields in TECHNICAL PHYSICS LETTERS

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two critical regions, namely, at the inner (closer to the PL axis) and outer (closer to the electrodes) boundaries of electron bunches. At the inner boundary, the background field and the field of electron bunches are oppositely directed (competitive). In this region, the method of verification of the trapping conditions is evident: the bunch field must be greater than the background field. Indeed, the results of probe measurements showed that the electric field of electron bunches at a distance of 17−25 mm from the axis is significantly (up to three times) greater than the background field (here and below, the numerical parameters refer to the results of experiments at ϕL = 1 kV in the SPD electrode configuration). The conditions of trapping at the outer boundary of the bunch are less critical, since the background field and the bunch field have the same directions. In order to check for this circumstance, we performed numerical simulations of electron trajectories in the central cross section of the PL for the experimentally measured field distributions. The results of these calculations showed that the conditions of trapping were sat1 isfied with considerable margin, and a chain of vortexed bunches was actually formed in the PL. In these vortices, electrons rotate around the centers at a velocity that is much greater than that of the electron bunch moving as a whole. The observed potential distributions and electron trajectories showed that vortices had a nearly elliptic shape elongated in the azimuthal direction and were 1–1.5 cm in size. The results of trajectory simulation showed that, in agreement with the condition of trapping at the inner boundary of the bunch, the vortices must disappear only at a wave amplitude about onethird of that observed in experiment. Additional experiments revealed high-frequency (≈70 MHz) small-scale oscillations, which were observed when a vortex passed by a probe (see regions indicated by arrows in Fig. 1c; Fig. 1f shows one of such regions on a greater time scale). The frequency of these oscillations measured in experiment was in satisfactory agreement with the calculated estimates of the vortex rotation velocity. Figure 1f also shows that, as expected, the frequency of these oscillations decreases at the vortex boundary, since the electron rotation velocity in the vortex must be at minimum near the separatrix. It should be noted that the frequency of electron rotation around the system axis in the background distribution is ≈10 MHz. Therefore, the velocity of the azimuthal motion of the observed structures is significantly lower than the background electron drift velocity and than the electron rotation velocity in the bunch. In terms of [4], such vortices can be classified as “slow.” Thus, we can ascertain that the observed anharmonic potential waves of large amplitude are manifestations of the large-scale, “slow” electron vortices that are developed in the PL volume as a result of the beam drift instability in the presence of a layered electron TECHNICAL PHYSICS LETTERS

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Fig. 2. Radial profiles of (1) the potential of the background electric field and (2) the maximum amplitude of oscillations (ϕL = 1 kV, SPD configuration).

density distribution. This statement is confirmed by the whole body of data, including: (i) the existence of regions where the potential wave field is significantly greater than the background field; (ii) the formation of localized vortexed bunches 1 revealed by simulations of the electron trajectories using the for the experimentally measured field distributions; (iii) satisfactory quantitative agreement between the frequency of small-scale oscillations observed when the electron bunch passes by the probe and the frequency of rotation obtained in the trajectory simulations; and (iv) the fact that the electron rotation velocity in a bunch is much greater than the velocity of the electron bunch moving as a whole. It should be noted that (see Fig. 2), the potential at the vortex center is close to the potential of an electrode from which the field lines passing through these regions originate (in the given case, this electrode is grounded). This implies that, under the experimental conditions studied, trapped electrons decrease the potential in this region down to the ground level and acquire the ability to go to the PL electrode because the longitudinal trapping condition is violated. As a result, the space charge accumulation ceases and the vortex amplitude is stabilized. The vortex amplitude can be also stabilized at the expense of electron loss in the direction across the magnetic field, provided that a sum of the force of inertia and the Coulomb force would exceed the Lorentz force. In this case, the vortex begins to smear and, in the limit of weak magnetic field, extends over the entire PL volume [4]. However, estimates showed that, under the experimental conditions studied, the number of electrons accumulated in vortices is insufficient to provide for the second mechanism, and the amplitude is stabilized according to the first mechanism.

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Acknowledgments. The authors are grateful to I.A. Soloshenko and V.I. Maslov for fruitful discussions and useful remarks. REFERENCES 1. A. I. Morozov and S. V. Lebedev, in Problems of Plasma Theory, Vol. 8: Plasma Optics (Atomizdat, Moscow, 1974), pp. 274–380 [in Russian]. 2. A. D. Grishkevich, A. M. Kapulkin, and V. F. Prisnyakov, in Ion Injectors and Plasma Accelerators, Ed. by A. I. Morozov and N. N. Semashko (Énergoatomizdat, Moscow, 1990), pp. 68–77 [in Russian]. 3. A. A. Goncharov, A. N. Dobrovolsky, A. V. Zatugan, et al., IEEE Trans. Plasma Sci. 21, 573 (1993).

4. A. A. Goncharov, V. I. Maslov, and I. N. Onishchenko, Fiz. Plazmy 30, 713 (2004) [Plasma Phys. Rep. 30, 662 (2004)]. 5. A. A. Goncharov and I. V. Litovko, IEEE Trans Plasma Sci. 27, 1073 (1999). 6. M. V. Nezlin and G. P. Chernikov, Fiz. Plazmy 21, 975 (1995) [Plasma Phys. Rep. 21, 922 (1995)]. 7. V. N. Gorshkov, A. A. Goncharov, and A. M. Zavalov, Fiz. Plazmy 29, 939 (2003) [Plasma Phys. Rep. 29, 874 (2003)]. 8. A. A. Goncharov, I. M. Protsenko, and Yu. M. Chekh, Ukr. Fiz. Zh. 50, 562 (2005). 9. I. G. Brown, Rev. Sci. Instr. 65, 3061 (1994).

Translated by P. Pozdeev

Spell: ok

SPELL: 1. vortexed

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