ISSN 1063-7842, Technical Physics, 2007, Vol. 52, No. 9, pp. 1217–1221. © Pleiades Publishing, Ltd., 2007. Original Russian Text © I.S. Zhirkov, V.A. Burdovitsin, E.M. Oks, 2007, published in Zhurnal Tekhnicheskoœ Fiziki, 2007, Vol. 77, No. 9, pp. 115–119.
ELECTRON AND ION BEAMS, ACCELERATORS
Influence of the Longitudinal Magnetic Field in the Accelerating Gap on the Limiting Parameters of a Plasma Electron Source Operating in the Forevacuum Pressure Range I. S. Zhirkov, V. A. Burdovitsin, and E. M. Oks Tomsk State University of Control Systems and Radioelectronics, pr. Lenina 40, Tomsk, 634050 Russia e-mail:
[email protected] Received November 11, 2006
Abstract—Results are presented from experimental studies of the influence of the longitudinal magnetic field in the accelerating gap on the emission current, accelerating voltage, and maximum gas pressure in a plasma electron source generating a continuous electron beam in the forevacuum pressure range. It is shown that the magnetic field in the beam-formation region stabilizes the emitting boundary of the plasma in the accelerating gap, thereby considerably improving the source parameters. PACS numbers: 52.50.Dg DOI: 10.1134/S1063784207090186
INTRODUCTION Filament-free electron sources with a plasma cathode are capable of efficiently generating electron beams in the pressure range from high vacuum up to forevacuum pressures (1–10 Pa) [1, 2]. From the standpoint of generating steady-state fast electron beams at such high pressures, devices of this type have no real alternative. Extension of the operating range of plasma electron sources toward higher pressures requires, first of all, increasing the electric strength of the accelerating gap. Previous studies of the generation of electron beams in the forevacuum pressure range showed that, in this case, along with the conventional interelectrode breakdown, the so-called “plasma breakdown”—the penetration of the plasma from the discharge region into the accelerating gap, the bridging of the gap by this plasma, and the subsequent switching of the discharge current from the anode to the accelerating electrode—can also take place [3]. The effect of the switching of the discharge current was thoroughly examined by Zharinov et al. [4, 5]. The limiting emission parameters at which the plasma cathode can stably operate obviously correspond to the complete switching of the discharge current. When these parameters are exceeded even slightly, plasma breakdown occurs. It was shown in [4, 5] that, for such switching to occur, it is necessary that the area of the electron collector (in our case, the area of the emitting plasma surface) be larger than a certain limiting value at which the chaotic electron current from the plasma becomes equal to the discharge current. Therefore, the required electric strength of the accelerating gap can be ensured by restricting the area of the emitting plasma surface. This
can be achieved, e.g., by creating a longitudinal magnetic field in the region of electron extraction and acceleration. This method is well known and is widely used in so-called magnetically insulated diodes to generate high-current pulsed electron and ion beams [6]. The present study is aimed at investigating the influence of the longitudinal magnetic field on the limiting parameters of a plasma electron source generating a continuous electron beam in the forevacuum pressure range. 1. EXPERIMENTAL SETUP The experiments were performed with a hollowcathode plasma electron source generating a narrow electron beam in the forevacuum pressure range. The design and operating principle of the source were described in detail in [7]. The main parameters of the continuously operating source were as follows: the working-gas pressure was 1–10 Pa, the discharge current was 0.1–1.0 A, the electron beam current was 30– 100 mA, and the accelerating voltage was 5–15 kV. A schematic of the discharge–emission unit is shown in Fig. 1, which gives an idea of the experiment and the physical model proposed. The discharge system consists of hollow cathode 1 with an output aperture of diameter D = 8 mm and flat anode 2 with a central emission opening of diameter d = 1.2 mm. Accelerating electrode 3 is placed at a distance of 5–7 mm from the anode and is electrically insulated from it by insulator 4, made of transparent glass for visual observations. Plasma 6 penetrates through the anode emission opening into the accelerating gap and forms there an emis-
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D
ϕ, V 4
(a)
3 4
2
d 1
Bz 6 5
2 0
2rp
–1 3 –2
Fig. 1. Schematic of the discharge–emission unit of the electron source.
sion surface of radius rp. The parameters of the penetrating plasma were measured with 16 single Langmuir probes 5, which were made of 0.4-mm-diameter tungsten wire and were introduced into the gap through the insulator wall. The plasma density was determined from the ion saturation branch of the probe current– voltage characteristic. The plasma potential was measured with a thermoprobe introduced into the emission channel from the side of the accelerating gap. The plasma potential with respect to the anode was determined from the point at which the current–voltage characteristics of the hot and cold probes began to diverge. The axial magnetic field with an induction of Bz = 0–15 mT was created by a solenoid that enclosed the discharge–emission unit. When the plasma electron source operates in the forevacuum pressure range, it is practically impossible to create a pressure difference between the regions of plasma generation and electron beam acceleration. Therefore, the experiments were carried out without gas puffing into the cathode cavity. When it was necessary, the pressure could be increased by supplying the working gas (air) directly into the vacuum chamber. 2. EXPERIMENTAL RESULTS The measurements show that an increase in the axial magnetic field appreciably reduces the plasma potential at the system axis, just near the anode emission opening (Fig. 2a). As the axial magnetic field is increased, the plasma density first increases and then reaches saturation (Fig. 2b). The measured density distribution of the plasma penetrating through the emission opening into the accelerating gap indicates that the magnetic field hampers the radial plasma expansion, confining it near the system axis. These results coincide with those obtained in [8] for a plasma ion source and, on the
0
2
4
n, 1011 cm–3 9.0
6
8
(b)
8.5
8.0
7.5
7.0
0
3
6
9
12
15 Bz, mT
Fig. 2. (a) Plasma potential ϕ and (b) plasma density n at the output of the emission channel as functions of the magnetic induction. The discharge current is 400 mA, and the gas pressure is 5 Pa.
whole, agree with the modern concept of plasma behavior in a magnetic field. The distributions presented in Fig. 3 were measured at a zero voltage across the accelerating gap. Visual observations show that, after applying the accelerating voltage, the glow of the penetrating plasma becomes brighter and the diameter of the glowing region increases. This indicates the intensification of the ionization processes. Applying the accelerating voltage results in the generation of an electron beam, whose current Ib, measured at a grounded collector installed beyond the accelerating gap, increases with increasing gas pressure (Fig. 4). When the gas pressure exceeds a certain threshold value, the beam generation terminates abruptly and a TECHNICAL PHYSICS
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INFLUENCE OF THE LONGITUDINAL MAGNETIC FIELD h, mm 0
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Ib, mA 60
(a)
4
45
10 1.6
3 30
20
2 1
1.0 0.8 1.2
15
0.4
30
0.2 × 1010 cm–3
40
0
4
5
6 P, Pa
Fig. 4. Electron beam current Ib as a function of the gas pressure P for different magnetic fields: (1) 1, (2) 5.3, (3) 7, and (4) 10 mT. The diameter of the emission opening is d = 1.2 mm, the accelerating voltage is Ua = 1 kV, and the discharge current is 400 mA.
(b) 1.3
10
Bz, mT 1.0 0.8 0.6
15
0.4
20
0.2 × 1010 cm–3 10
30
5
40
0 50
0
2.5
5.0
7.5
10.0 R, mm
5
6
7
8 P, Pa
Fig. 3. Contour lines of the density of the plasma penetrating through the emission opening into the accelerating gap in the plane of the axial and radial coordinates (h and r) for magnetic inductions of (a) 4 and (b) 15 mT. The gas pressure is P = 6 Pa, and the discharge current is ID = 300 mA.
Fig. 5. Minimum magnetic induction Bz required to prevent breakdown as a function of the gas pressure P for different discharge currents ID: () 500, () 600, and () 700 mA. The diameter of the emission opening is d = 1.2 mm, and the accelerating voltage is Ua = 1 kV.
bright glow appears in the accelerating gap. This is accompanied by a decrease in the voltage across the accelerating gap and a jump in the current in the power supply circuit. All this allows us to assume that the effects observed are related to the gap breakdown. It can be seen from Fig. 4 that the limiting pressure at which the beam generation terminates increases with increasing magnetic induction. The minimum induction that is required to prevent gap breakdown increases with increasing discharge current (Fig. 5), i.e., with increasing plasma density (Fig. 2b). The visually observed plasma glow in the accelerating gap indicates that the penetrating plasma is affected by the magnetic
field to a larger extent than the propagating electron beam.
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3. DISCUSSION OF THE RESULTS OBTAINED As was noted above, the observed plasma breakdown of the accelerating gap can be caused by the penetration of the plasma from the discharge region into the accelerating gap and the subsequent switching of the discharge current from the anode to the accelerating electrode. The condition for such switching can be writ-
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n, 1012 cm–3 7
1
6
2
electrons. The ions escape from the plasma in the axial direction toward the anode, whereas the electrons are emitted in the form of a beam. The radial plasma density distribution can be calculated by solving the continuity equation for the radial particle flux. Since the plasma behavior is mainly determined by its heavier (slower) ion component, it is sufficient to consider the continuity equation for ions. In cylindrical coordinates, this equation has the form
5 3
4 3
nv i 1 d dn D ⊥ --- ----- ⎛ r ------⎞ = – W i + --------. r dr ⎝ dr ⎠ l
2 1 0
2
4
6
8
Here, n is the plasma density; Wi is the rate of ion generation by plasma electrons (i.e., the number of ionization events per unit volume per unit time); nvi/l is the rate at which the ions escape toward the anode; vi is the Bohm velocity; l is the axial plasma length; D⊥ is the coefficient of ion diffusion across the magnetic field,
10 Bz, mT
Fig. 6. Calculated limiting plasma density n at the system axis as a function of the axial magnetic field Bz for different gas pressures: (1) 3, (2) 6, and (3) 9 Pa.
ten as [4] fG ≥ 1,
(1)
where f = Se/(Se + Sa) is the ratio of the area of the emitting plasma boundary Se to the sum of Se and the anode area Sa. Taking into account the actual electrode configuration (Fig. 1), the sum Sa + Se is equal to the crosssectional area of the cathode cavity πD2/4, because the working area of the anode surface is determined by this cross section and Se is the area of the emitting plasma boundary π r p . The factor G is the ratio of the density of the chaotic plasma electron current jc to the anode current density j, 2
e ( ϕ p – ϕ a )⎞ j - , G = ----c = exp ⎛ -----------------------⎝ ⎠ kT j
(3)
(2)
where ϕp and ϕa are the plasma and anode potentials, respectively. Expression (1) indicates that the current switching occurs when the area of the emitting plasma boundary becomes larger than a certain critical value. The fact that the radial expansion of the plasma penetrating into the accelerating gap is limited by the longitudinal magnetic field allows one to express the switching condition through the magnetic induction, the plasma density, and the area of the emitting plasma boundary. The physical model describing plasma penetration into the accelerating gap through the anode emission opening is based on the following assumptions, whose validity is proved experimentally. The plasma is homogeneous in the axial direction. The plasma density at the axis is determined by the parameters of the hollow-cathode discharge, in particular, by the discharge current. The radial expansion of the plasma is due to ambipolar diffusion. Ion–electron pairs are generated by plasma
D0 D ⊥ = ----------------------------------, 1 + ( λ i λ e /r i r e )
(4)
where D0 is the ambipolar diffusion coefficient in the absence of a magnetic field; λi and λe are the ion and electron mean free paths, respectively; and ri and re are the ion and electron cyclotron radii, respectively. When the dependence of the ionization cross section on the electron energy can be approximated by a linear function, the expression for Wi has the form 8kT 1/2 eϕ 2kT W i = n n ⎛ -----------e⎞ α i exp ⎛ – --------i ⎞ ⎛ ϕ i + -----------e⎞ n, ⎝ πm ⎠ ⎝ kT e⎠ ⎝ e ⎠
(5)
where nn is the density of neutral particles, ϕi is the ionization energy, n is the electron density, Te is the electron temperature, and αi is the coefficient in the linear approximation. It is clear that, in order to determine l, it is necessary to calculate the length of the space charge sheath separating the plasma from the accelerating electrode and to calculate l as a small difference between two large quantities: the interelectrode distance and the sheath length. Since the accuracy of such calculations is poor, the quantity l was assumed to be constant and equal to 1 mm, taking into account that the diameter of the emission opening is of the same order of magnitude. Equation (3) allows one to calculate rp. Substituting rp into condition (1), we find the relationship between the plasma density at the system axis and the required magnetic field. The results of calculations presented in Fig. 6 are in qualitative agreement with the measured dependences. This is evidence in favor of the proposed mechanism for the influence of the magnetic field on the limiting parameters of the plasma electron source. TECHNICAL PHYSICS
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INFLUENCE OF THE LONGITUDINAL MAGNETIC FIELD
CONCLUSIONS
REFERENCES
Applying a longitudinal magnetic field to the accelerating gap of a plasma electron source allows one to prevent breakdown and to increase the limiting values of the emission current and gas pressure. The physical reason for this effect is the radial confinement of the plasma penetrating from the discharge region into the accelerating gap and the restriction of the area of the emitting plasma surface. This prevents the switching of the current from the anode to the accelerating electrode and, therefore, the jump in the discharge current and the drop in the voltage drop across the accelerating gap. ACKNOWLEDGMENTS This work was supported by the Russian Foundation for Basic Research (project no. 05-08-013119) and INTAS (grant no. 06-1000016-6254).
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1. V. A. Burdovitsin, Yu. A. Burachevskii, E. M. Oks, et al., Izv. Vyssh. Uchebn. Zaved., Fiz. 44 (9), 85 (2001). 2. V. A. Burdovitsin, Yu. A. Burachevskii, A. V. Mytnikov, and E. M. Oks, Zh. Tekh. Fiz. 71 (2), 48 (2001) [Tech. Phys. 46, 179 (2001)]. 3. V. A. Burdovitsin, M. N. Kuzemchenko, and E. M. Oks, Zh. Tekh. Fiz. 72 (7), 134 (2002) [Tech. Phys. 47, 926 (2002)]. 4. A. V. Zharinov and Yu. A. Kovalenko, Zh. Tekh. Fiz. 56, 681 (1986) [Sov. Phys. Tech. Phys. 31, 410 (1986)]. 5. A. V. Zharinov and Yu. A. Kovalenko, Izv. Vyssh. Uchebn. Zaved., Fiz. 44 (9), 44 (2001). 6. A. V. Agafonov, V. P. Tarakanov, and V. M. Fedorov, Zh. Tekh. Fiz. 74 (1), 93 (2004) [Tech. Phys. 49, 93 (2004)]. 7. V. A. Burdovitsin, I. S. Zhirkov, E. M. Oks, et al., Prib. Tekh. Éksp., No. 6, 66 (2005). 8. M. D. Gabovich and E. T. Kucherenko, Zh. Tekh. Fiz. 26, 997 (1956).
Translated by É. Baldina
