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ОСНОВНОЙ РАЗДЕЛ
Hussein A.M.
University of Anbar, College of education for pure Sciences, Physics
Department
INVESTIGATION OF HIGH-FREQUENCY POWER ABSORPTION IN A
DENSE PLASMA COLUMN
Статья посвящена исследованию поглощения высокочастотной мощности в столпе густой плазмы, с параметрами, характерными для индуктивно связанной плазмы. Для определения ВЧ мощности использовалось решение краевой задачи для уравнений Максвелла. В качестве механизма диссипации энергии ВЧ поля учтено поглощение за счет столкновений и затухания Ландау. Установлено, что величина локальной ВЧ мощности, поступающей к электронному компоненту плазмы, влияет на температуру электронов и, как следствие, на локальную скорость ионизации, которая определяет эволюцию плотности плазмы.
Ключевые слова: ВЧ, плазма, мощность, частота, индукционный источник.
The article is devoted to the study of high-frequency power absorption in a dense plasma column, with parameters characteristic of inductively coupled plasma. To determine the high-frequency power, the solution of boundary-value problem for Maxwell equations is used. As a mechanism for HF field energy dissipation, absorption is taken into account due to collisions and Landau damping. It is found out that the value of local HF power entering the electronic component of plasma affects the electron temperature and, as a consequence, the local ionization rate, which determines plasma density evolution.
Keywords: HF, plasma, power, frequency, induction source.
Induction sources of plasma attract great attention as tools meeting modern microelectronic industry requirements. They are able to work both with an external magnetic field (helicon wave plasmas) and without it (transformer coupled plasmas) [1]. Induction sources make it possible to generate dense low-temperature plasma in a wide range of magnetic fields, working gas pressures and excitation frequencies, and also have dimensions from centimeters to meters and are excited by sufficiently simple antennas with relatively low power consumption.
Investigation of induction sources of plasma is carried out in many laboratories in Australia, Korea, Germany, the USA, France, Japan and other countries and is of great applied and fundamental importance. The sphere of practical applications of these sources includes terrestrial and space technologies, such as: precision surface treatment of materials, deposition of thin films and coatings, surface cleaning and creation of nanostructures. The most complete
information about dielectric characteristics of plasma and wave-particle interaction can be obtained by solving kinetic equations for the distribution function of charged particles in the phase space.
Imposition of the magnetic field improves operating characteristics of the source. In particular, it increases plasma load impedance, leading to increase in discharge efficiency and stability. This means that HF power absorption mechanisms significantly change in a magnetic field [2]. To identify these mechanisms, a model experiment on the absorption of low-power HF signal in dense plasma was carried out.
The experimental installation shown in Fig. 1, is similar to a typical helicon source [3,4]. It includes a quartz discharge chamber, on which a magnetic field up to 300 G can be superimposed, and a metal drift chamber. The system is filled with plasma with a density of up to 2x1012 cm-3 from pulsating ECR discharge and is ignited by a magnetron with an operating frequency of 2.45 GHz and power of up to 0.5 kW.
Fig. 1 The scheme of experimental helicon source
1-gas-discharge chamber; 4-ion-optical system;
2-HF antenna; 5-emission hole of the ion-optical system;
3-permanent magnet system; 6-gas inlet.
The penetration of SHF power from the magnetron into the HF excitation volume is prevented by means of a wire mesh, and the penetration of a strong magnetic field is prevented by means of a screen. The HF antenna has an azimuthal symmetry m = ± 1 (Nagoya type), or m=0 (single-circuit), and is fed through a matching device from a low-power HF generator at a frequency of 8-26 MHz
The instantaneous plasma density is measured with an 8-mm interferometer. At first, a helicon wave arises in plasma. Then the helicon wave generates Trievelpiece-Gould wave. The TG-wave energy is well absorbed by plasma due to the mechanism of electron-neutral and electron-ion collisions or due to Landau
damping of Trievelpiece-Gould wave. The helicon wave arises in plasma when 2ro~roce. With a power input of about 120 watts, the ion current density can reach 100 mA / cm2.
Electromagnetic fields are described by Maxwell's equations with dielectric permittivity tensor in hydrodynamic approximation, which takes into account particles collision and external current of the antenna [5]. To find stationary solutions of these equations, we use the normal modes method, which makes it possible to reduce the problem to a one-dimensional task (with respect to a radial variable). In accordance with this method, the electromagnetic fields and current density of the antenna are decomposed along longitudinal and azimuthal coordinates into Fourier series with amplitudes that depend on the radius.
B
JA J
=z
f Er sin kzл
Br cos kz J, sin kz
J Ar J
+ ,
Ee'sin kz B cos kz
JAe(r)sin kz
+ <
E sin kz
B cos kz
J „ (r) sin kz
J AzK '
expp—i at+ime )
e
r
z
l ,m
where k=lx /L (l =0,1,2,..., L- source length) and m =0,±1,±2,... are longitudinal and azimuthal wave numbers. Ordinary differential equations obtained for field amplitudes are solved with regular boundary conditions on leading surfaces of joining conditions, on interfaces of the media and antenna location.
Investigation of a fast magnetosonic wave (with ro>roci) and fast Alfven wave (with ro<roci), excited by azimuthal currents of the antenna at plasma periphery, is expedient to carry out on the basis of two-dimensional calculations of propagation regions (N2^F>0, ge N2^F= ((ei-N2|| )2-e22)/(e1-N2\\) - fast-wave dispersion equation) and conversion zo nes (N2||=e1) of the fast wave with a fixed longitudinal refractive index N as well as on the basis of estimates made
using experiments parameters and magnetic field calculations according to Bio-Savart laws. Figures 2 and 3 show calculated regions of the fast wave propagation for different plasma density values at the center for the toroidal harmonic l=10.
20 r ' 80 85 90 95 100 1 05 ПО 115 120
li (cm)
Fig. 2 Shaded area - fast-wave propagation zone; C - the last closed magnetic surface, A -schematic antenna display, H - ion cyclotron resonance, dotted lines - normalized magnetic field strength module no=8х10uсм-3
Fig. 3 Shaded area - fast-wave propagation zone; C - the last closed magnetic surface, A - schematic
antenna display, H - ion cyclotron resonance, dotted lines - normalized magnetic field strength module no=1,4х1013см-3
From Fig. 2 and 3 it is clear that with increasing plasma density the region of fast wave propagation narrows and shifts to the periphery.
The model profile of the plasma density was calculated by the formula:
n( x) =
4i _ AiW
¥<¥i
e -i
nP + k - nP U¥¥'л ¥i^¥>¥i
& _ A-W
nb + (no2 - т) ^^V ¥>¥i e -1
where y = y(x) - magnetic surface mark, n0 - central density, nb - ultimate density, np - pedestal density, £1,£2,AA,y- parameters that define the profile shape. Modeling the density profile using such a formula allows one to separately vary both main part parameters and pedestal parameters on plasma edge.
The dependence of plasma resistance on density contains a series of absorption peaks, which are interleaved with minima. It is this non-monotonic dependence that follows from the theory explaining effective absorption of HF power in the helicon source due to the surface conversion of helicon waves directly excited by the antenna to electrostatic waves [6]. This theory explains the dependence of plasma resistance on its density in the following form:
Rp « R BF
L n
/
n
RLfn B
where n - plasma density,
B - external magnetic field strength,
f - excitation frequency,
L, R- length and radius of the plasma column,
F- non-monotonic function of its argument.
It is seen from the above formula that when other parameters are constant, with increasing B the resistance peaks are shifted with a constant velocity towards a higher density without changing the amplitude. If the excitation frequency changes with a constant magnetic field, the resistance peaks move toward lower density with simultaneous amplitude increase.
Absorption peaks values can be controlled by means of the antenna. Peak amplitudes behavior agrees with theoretical idea that power contribution to plasma is due to antenna interaction with different spatial modes of waves with proportionality coefficients of cos2(2nz / Xz), where Xz is the longitudinal mode wavelength, a z is ring position coordinate.
The experimental data indicate that plasma resistance over a wide range does not depend on working gas pressure. This indicates that HF power is absorbed by collective mechanisms, one of which is wave conversion, and not electron collision as it is described in theoretical concepts.
In addition, experimental data indicate that, under these conditions in addition to surface conversion of waves, another non-resonant mechanism of
power absorption operates, which can be identified with absorption due to capacitive coupling of the antenna to plasma. Analysis shows that other collective mechanisms are ineffective under experimental conditions. Indeed, waves' emission into remote plasma region is screened by a metal mesh, and volumetric conversion is ineffective in fields greater than 100 G due to weak radial inhomogeneity of plasma column.
References:
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3. Increase of helicon discharge efficiency in the convergent magnetic field / V.F. Virko, K.P. Shamray, G.S.Kirichenko [et al.] // Problems of atomic science and technology. - 2005. - №4. - P. 241 - 246.
4. Helicon source of ions in high-density plasma mode / S.N. Mordik, V.I. Voznyi, V.I. Miroshnichenko [et al.] // Problems of atomic science and technology Series: Plasma electronics and new methods of acceleration. - 2006. - №5. - P. 208-212.
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