Formation of a trap in the dusty plasma of photovoltaic atomic battery

Transcription

1 nd International Symposium on Plasma Chemistry July 5-, 5; Antwerp, Belgium Formation of a trap in the dusty plasma of photovoltaic atomic battery A.V. Filippov, A.F. Pal, A.N. Starostin and V.. Cherkovets SRC RF Troitsk Institute for Innovation and Fusion Research, Troitsk, Moscow, Russia Abstract: Formation of a dusty plasma trap in a non-self-sustained gas discharge controlled by alectron beam is studied. Dust particle charge is defined by taking into account the nonlocality of the electronergy distribution function (DF). It is obtained that for the given gas ionization rate and the applied discharge voltage dust particles have a critical size above which their sedimentation on the cathode occurs. Keywords: non-self-sustained gas discharge, electron beam, dusty plasma, cathode sheath. Introduction The interest to the dusty plasma under pressures of ~ bar has been raised quite recently and is basically connected with studying the possibility of developing autonomous energy sources on the basis of plasma-dusty structures [, ]. The operation of such anergy source bases on plasma created by the products of dust radionuclides particles decay and requires that the ordered structure from dusty particles be created. The non-selfsustained discharge controlled by axternal electron beam appeared to be most suitable tool for experimental modeling of such plasma. Therefore, the present paper reports the results of the work on studying the dusty plasma excited by a fast electron beam under atmospheric or higher pressures.. Self-consistent model of the non-self-sustained discharge The self-consistent model of the non-self-sustained discharge from [3] by taking into account the processes of electron and ion losses owing to the sink to dust particles as well as hydrodynamic equations for the neutral component was developed. Such model is described by the following equations: ne + je = Qion + nionne βein e βde Zd ndne, ni + ji = Qion + nionne βein e βdi Zd ndni, nd + ( ndvd) =, Vd p 6pηr + = mn d d md ezd + g+, m d ( Vd ) Vd ( Vd Vg) d ( ) () () φ = πen n+ Zn, = φ, (3). i e d d ere je = De ne µ ene, ji = µ ini,, are the electron and ion number densities, is the electric field strength, µ e, µ i are the mobilities of electrons and ions respectively, D e is the electron diffusion coefficient, β de, β di are the recombination coefficients of electrons and ions on dust particles with the charge, Q ios the bulk gas ionization rate by axternal source, os the frequency of the gas ionization by plasma electrons, β ei is the coefficient of electron-ion recombination, V d and V g are the velocities of the directed movement of dust particles and gas, g is the acceleration of gravity, ln ( µ ene µ ini) Zd ( ne ni r) = Zdr ln ( µ e µ i) β π eµ β β,,, =, =, di i de di is the charge of a dust particle having a µm radius with takento account the DF non-locality [], r is the radius of dust particles in micrometre. Let us apply the following boundary conditions to system (-3) (the cathode is at z =, the anode is at z =, U dis is the discharge voltage applied to the electrodes, v Te is the thermal velocity of electrons, γ is the coefficient of the secondary ion-electromission from the cathode): ( γ ) nv = kn + kn, n = ; e Te z= e e i i z= e z= n = ; V =, n = ; φ i z= d z=, z= d z=, z= =, φ = U, z= z= Let us assume the following initial conditions:, Udis n =,,, e n = i = z V t t t t t d t φ = = = = = = = = Nd 3 3 z 3 nd = 56 ( 8 8 ) ( ), V y y + θ y y =, t= dis where V dis is the discharge volume, N d is the number of dust particles injected into the discharge; θ(x) is the step function. According [3], the gas ionization transverse directios rather homogeneous. Therefore, it is possible to consider the problem within one-dimension approximation along the z-axis. We can also assume that dis P-II-7-3

2 electron transfer coefficients and the coefficient of electron-ion recombination are constant (this is justified since the field in the positive column under the considered regime is weak [3], and the electron number density in the near-cathode layer is small). The z-axis is directed upwards. In the steady regime the gas velocity is equal to zero. The typical velocity relaxation time of dust particles considerably exceeds their typical number density time setting, therefore, it is possible to neglect their inertia and to define their velocity from the stationary equation of their movement. Let us solve the equations in system (-3) in the following way. Firstly, we solve the electron number balance equation by the iteration method (by the sweep method according to the Crank Nicolson scheme) and the Poissoquation (by the sweep method) with using the electron number densities which were determined at this iteration. Then we solve the number balance equation for ions according to the explicit scheme with using the directed differences to determine the drift members. After this, we solve the equation of continuity for a dusty component. a),i - (cm -3 ) n d (kv/cm) (V/cm) Numerical simulation results and discussions The simulation results of dusty trap formation presented in Figs. -5. It is seen Fig. how a dusty particle trap for charged dusty particles forms. Fig. b shows the distributions for dusty particle charge and the electric field in the levitation area in a larger scale. The ionization rate for xenon at atmospheric pressure and room temperature was assumed to be equal to Q ion = cm -3 s -, the voltage U dis = kv was applied to the discharge gap. N d = 5 5 particles of r = 5 µm were injected into the discharge area. It is seen Fig. how a disk-like dusty particle structure where all the plasma parameters remained practically constant is formed. In Fig. there are analogous distributions for a non-self-sustained discharge in argon. Comparison of Figs. and shows considerable difference in the behavior of positive ion number density in the near-cathode layer: in xenon is greater in the near-cathode layer than the positive column, and in argon the ion number density is significantly lower in the near-cathode layer than the positive column. This is due to the following fact. Balance equation of positive ions () in the steady regime results in the following: j = Q β Z nn () i ioi e i id d d i Taking into consideration the equality of the ion number density gradient in the discharge gap to zero practically everywhere, we caxpress the divergence of the positive ion flux in the following way: b) Fig.. Steady distributions for electron ( ) and ion ( ) number densities, a dusty component charge (n d ) ilementary charge units and the electric field strength () in the discharge gap in xenon at Q ion = cm -3 s -, U dis = kv, N d = 6, r = 3 µm, ρ d =.9 g/cm 3. - n (cm -3 ) (kv/cm) n d. Fig.. Steady distributions for electron ( ) and ion ( ) concentrations, a dusty component charge (n d ) ilementary charge units and the electric field -5 P-II-7-3

3 strength () in the discharge gap in argon at Q ion = cm -3 s -, U dis = kv, N d = 3 5, r = 5 µm, ρ d =.9 g/cm 3. P-II-7-3 3

4 Comparison of Figs. and shows considerable difference in the behavior of positive ion number density in the near-cathode layer: in xenon is greater in the near-cathode layer than the positive column, and in argon the ion number density is significantly lower in the near-cathode layer than the positive column. This is due to the following fact. Balance equation of positive ions () in the steady regime results in the following: j = Q β Z nn (). i ioi e i id d d i Taking into consideration the equality of the ion number density gradient in the discharge gap to zero practically everywhere, we caxpress the divergence of the positive ion flux in the following way: ji ( kn i i) = kn i i + ki ni (5). kn = π ekn n n ( ) i i i i i e The Poissoquation (3) was used in the final step in (5). Using (5) with the negativity of the charge of levitating dusty particles, we have from () the following: ( ) Q β n n n =. ioi e i id i i e In the positive column, therefore, from (5) we obtain n = Q β. (6). i, pc ioi In the near-cathode layer, therefore, n = Q β. (7). i, sh iod We can see from the Table that in xenolectron-ion and Langevin recombination coefficients are very close to each other, therefore, the ion number densities in the positive column and in the near-cathode layer are also close. In argon β id is more than four times greater than β ei, therefore, the ion number density in the positive colums approximately times greater than that in the near-cathode layer. In Fig. 3 there is distribution of the electron and ion number densities, dusty particle charges and electric field strength in the non-self-sustained discharge in xenon under injecting dusty particles of two sizes. In this case two equations of continuity and motion were solved for the particles of each size. a),i - (cm -3 ) n d..5. (V/cm) -75 n d (kv/cm) In Table the electron-ion (β ei ) and Langevin (β id ) recombination coefficients, ion number densities in the near-cathode layer (,sh ) from (7) and in the positive column (,pc ) according to (6) in the non-self-sustained discharge in heavy inert gases at atmospheric pressure are presented Table. Parameters of the dusty plasma created by e-beam. Q ion, cm -3 s - β ei, cm 3 /s β id, cm 3 /s n, Газ,sh, cm -3 i,pc cm Ar Kr Xe b)..5. Fig. 3. Distribution of the electron and ion number densities (a), dusty particle charge (b) and electric field strength in the non-self-sustained discharge for r = µm, N d = 6, r = 3 µm, N d = N d /3, ρ d = ρ d =.9 g/cm 3. Fig.3 illustrates how the separation of different sized particles in height occurs in the cathode layer. Let us note anteresting feature in the distribution of the electric field strength and the number density of dusty particles: in the levitation area of dusty particles they appear to be practically constant. It is seen Fig. 3 that larger particles levitate in the area with the greater field than P-II-7-3

5 small ones. In Fig. there is distribution of the modified nonideality parameter in the discharge gap in the non-selfsustained discharge in argon at various applied voltages. Γ Calculation shows that the critical radius also increases when the applied voltage to the discharge is increased. N d Fig.. Modified nonideality parameter Г * in argon at Q ion = cm -3 s - as a function of the height over the cathode. Curve is for U dis = 5 V, is for V, 3 is for 5 V, is for V. The modified non-ideality parameter Γ * is defined by the following expression [5]: ( κ κ ) * Γ =Γ + + e κ where Γ is the non-ideality parameter: Γ = e /at d, T d is the temperature of the dusty component inergetic units, κ is the structural parameter: κ = k sh a, k sh is the screening constant, a is the average interparticle distance: a = n d -/3, n d is the density of dust particles. Fig. illustrates that in the disk-like structure the dusty component is a liquid, the nonideality parameter decreasing with the growth of the voltage, which is due to the decrease in dusty cloud density (it is seen Fig. that when the applied voltage grows the width of the dusty cloud increases, which leads to the decrease in the density in case the total number of particles is constant). The total number of dusty particles in the discharge area considerably depends on the radius of dusty particles. It appears that for the given dust material density, gas ionization rate and applied voltage the dusty particles have a critical radius above which all the particles injected into the discharge area deposit on the cathode. As axample, Fig. 5 shows that when the radius grows there remains less and less particles in the discharge gap in the stationary regime, while the particles with the radius of µm and larger cannot levitate in the non-selfsustained discharge in xenon at the given parameters at all. Table shows the sizes of particles still levitating in the discharge area while the particles whose radius is.5 µm larger deposit upon the lower electrode within about s. It is seen that the growth of the gas ionization rate is accompanied by the growth of the critical radius... t (s) Fig. 5. Time evolution of the total number of dust particles N d in xenon, Q ion = 5 cm -3 s -, U dis = kv. Curve r = µm,.5 µm, 3.75 µm, - µm. Table. The largest size (in µm) of levitating dust particles with ρ d =.9 g/cm 3 at U dis = V. Q ion cm -3 s Argon Krypton.5 7 Xenon Conclusions It is shown on the basis of the self-consistency model of the non-self-sustained discharge inert gases how a trap for dust particles forms. It is obtained that for the given gas ionization rate and the applied discharge voltage the dust particles have a critical size above which their sedimentation on the cathode occurs. 5. Acknowledgments The work was supported by the State Atomic nergy Corporation Rosatom (contract no. Н.х ) and a grant from the President of the Russian Federation (no. NSh-93..). 6. References [] V.Yu. Baranov, A F. Pal, A.A. Pustovalov, et al. in: Isotopes: Properties, Production, Application. (V.Yu. Baranov; d.) (Moscow: Fizmatlit), Vol., 59 [in Russian] (5) [] A.V. Filippov, A.F. Pal', A.N. Starostin, et al. Ukr. J. Phys., 5, 37 (5) [3] A.V. Filippov, V.N. Babichev, N.A. Dyatko, et al. JTP,, 3 (6) [] A.V. Filippov, N.A. Dyatko and A.S. Kostenko. JTP, 9, 985 () [5] O.S. Vaulina and S.A. Khrapak. JTP, 9, 87 () P-II-7-3 5