Injection of small macroscopic particles into plasmas as a diagnostic techniqueT. C. Anestos and C. D. Hendricks Citation: Journal of Applied Physics 45, 1176 (1974); doi: 10.1063/1.1663385 View online: http://dx.doi.org/10.1063/1.1663385 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/45/3?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Fast gas injection as a diagnostic technique for particle confinement time measurements Rev. Sci. Instrum. 77, 10E901 (2006); 10.1063/1.2219379 Manipulation of the magnetic state of a small ferromagnetic particle by means of nonlocal spin-injection techniques(invited) J. Appl. Phys. 99, 08G506 (2006); 10.1063/1.2162031 Microwave diagnostics of small plasma objects J. Appl. Phys. 98, 033301 (2005); 10.1063/1.1996835 Diagnostics and modeling of a macroscopic plasma display panel cell J. Appl. Phys. 88, 3905 (2000); 10.1063/1.1308094 Plasma potential profile determination by a new diagnostic based on neutral particle beam injection and laserinduced fluorescence Rev. Sci. Instrum. 70, 908 (1999); 10.1063/1.1149328

[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 129.174.21.5

On: Mon, 22 Dec 2014 04:11:24

Iniection of small macroscopic particles into plasmas as a diagnostic technique

T. C. Anestos and C. D. Hendricks

University of Illinois, Urbana-Champaign, Illinois 61801 (Received 1 October 1973)

A method is presented for the determination of electron temperature of plasma by the measurement of the charge acquired by a small spherical macroscopic particle of the order of 20-25 !J. in diameter as it travels through the plasma. The particles are generated by the electromechanical breakup of a liquid jet. A theoretical relation between the electron temperature and the particle charge is derived which allows the determination of the electron temperature after the charge of the particle is measured experimentally. Measurements of the electron temperature in argon and helium plasmas are done, and comparisons with Langmuir probe measurements show good agreement.

I. INTRODUCTION

Recently, the possible use of macroscopic particles in some areas of plasma physics has become of interest. One of these areas is the fueling of thermonuclear fusion reactors, where serious consideration is given to the possibility of fueling the reaction by injecting macro­scopic deuterium particles. l ,2

Another area of application of macroscopic particle technology is in plasma diagnostics, where information about the plasma parameters can be obtained by injecting small particles into the plasma and measuring the re­sulting change of mass and charge. Charging of the particles could be a significant factor in changing the rate of evaporation of the particles. In a cold plasma the particles of low-vapor-pressure material will not lose significant mass, but they will gain some charge. In the experiment described in this paper, small macroscopic particles were injected into a plasma, and the electron temperature was determined by measuring the charge acquired by the particles.

II. CHARGING OF A PARTICLE IMMERSED IN A PLASMA

A body immersed in a plasma is continuously bom­barded by electrons and ions. Since the electrons have higher velocities than the ions, the electron current is initially much larger than the ion current and the body is charged negatively. Thus, the body repels electrons and attracts ions and, as a result, is surrounded by a positive space charge or positive sheath. The problem of electron and ion currents onto bodies of various geometries in a plasma was first studied fifty years ago by Mott-Smith and Langmuir. 3 The solution of the prob­lem involves two parts: first, the mechanical part, which involves the trajectories of the ions and electrons in the electric field of the particle, and, second, the space charge part, which involves the solution of the Poisson equation in the sheath region around the parti­cle. From the two relations which are obtained, the sheath radius can be eliminated and a single equation can be obtained expressing the current as a function of the potential of the particle.

Since the electrons are in repulsive force field, the rate at which they fall on the surface of the particle is

(1)

where me is the electron mass, Te is the electron tem-

1176 Journal of Applied Physics, Vol. 45, No.3, March 1974

perature, No is the undisturbed electron density, a is the radius of the particle, and cf>=ne/41T€oa is the poten­tial at the surface of the particle, with ne as the charge on the particle.

The ion current can be obtained from the following equation:

(2)

where s is the sheath radius, u and q are the radial and tangential velocity components at the edge of the sheath, respectively,

g{q, u) =~ (:i,) 3/2 exp [- 2:;1 (u2 + q2)], and ql' the upper limit of the integral, is the maximum value of the tangential component of the velocity of the ions which can still be captured by the particle.

The value of ql can be obtained from the equations of energy and angular momentum conservation,

(3)

and

aUa = su, (4)

under the conditions u> 0 and u~ > 0; then

eft =h (u2 + 2~). s -a m l

(5)

The ion current is given by

This equation involves the sheath radius, which is very difficult to determine. Bettinger and Walker4 have numerically solved Poisson'S equation and have obtained an empirical expression for the sheath radius as a function of the Debye length L:

(7)

However, under certain conditions Eq. (6) can be simplified and an expreSSion can be obtained which is independent of the sheath radius. This is the case when the radius of the particle is much smaller than the sheath radius. At this limit, a« s, the ion current becomes

Copyright © 1974 American Institute of Physics 1176

[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 129.174.21.5

On: Mon, 22 Dec 2014 04:11:24

1177 T.C. Anestos and C.D. He.ndricks: Small macroscopic particles into plasmas 1177

fi Iter holder oscillator

;)----____ electromechanical transducer

gloss to metal seal

2 magnetic coils

soft iron cylinder

~~~~~~~~~~-caPillary opening

tungsten wire

C=500

R=lon

V= 10 volts

FIG. 1. Particle generator.

In the system used for the experiments reported in this paper, the Debye length was about 100 Il and the radius of the particles was about 10 Il. Thus, Eq. (8) is valid.

(8)

At equilibrium the ion and electron currents to the particle surface are the same. If Eq. (1) and (8) are 'equated, we obtain the following expression for the po­tential of the particle as a function of the electron and ion temperatures:

( kTe)1/2exp(_lect>I)=( kTI)1/2(1+ lect>I). (9) 27Tme kTe 27Tml kTI

The dependence of the potential ct> on the ion tempera­ture is very weak; for example, for a 50% change of Tp the change in ct> is only 8%. On the other hand, the dependence of ct> on the electron temperature is almost directly proportional. Therefore, the electron tempera­ture can be determined from Eq. (9) be measuring experimentally the charge of the particle.

III. EXPERIMENTAL APPARATUS AND RESULTS

The method used for the production of small macro­scopic uniform particles is based on the breakup of a cylindrical liquid jet into uniform drops by vibrations applied to the jet, which becomes unstable under the action of surface tension. 5,6 An electromechanical transducer driven by an oscillator was used to generate the vibrations.

The capillary was made by heating a glass tube until its inside collapsed into a conical shape and then break­ing it after scratch.ing the surface with a diamond point. The production of liquid particles of 39 < 20- Il radius inside a vacuum presents certain problems. First, before the pressure is applied in order to force the liquid out ot the opening, the liquid drips out of the capillary opening and forms a liquid sphere in front of

J. Appl. Phys., Vol. 45, No.3, March 1974

the opening, which thus prevents the formation of the jet. Second, the capillary is easily clogged. In order to eliminate these problems, a microvalue made of a tungsten wire with a very fine tip and energized by mag­netic fields was constructed. In addition to eliminating these problems, the valve acts to turn the liquid jet off on electronically. The capillary system is shown in Fig. 1.

The experiment was performed in a glass vacuum system. The vacuum was maintained by an oil diffusion pump and a mechanical forepump. Argon gas was allowed to flow into the system until the pressure rose to 5 x 10-5 torr. The plasma was formed inside a coaxial cylindrical system 30 cm long. A thoriated tungsten wire about 5 cm long was stretched 0.5 cm outside, parallel to the inner cylinder, and was used for the thermal emission of electrons. The electron emitter was at the end of the cylinders into which the macro­scopic particles were injected. The electrons were accelerated towards the outer cylinder by a potential difference applied between the tungsten wire (and the inner cylinder) and the outer cylinder. An axial mag­netic field was used to increase the path of electrons and, therefore, the change of an ionizing collision be­tween a electron and an atom. The entire experimental setup is shown in Fig. 2.

Alcohol was selected as the working liquid for the formation of the uniform particles. The particles were inj ected into the plasma, and they then travelled along trajectories almost parallel to the axis in the space be­tween the two coaxial cylinders, where their charge was measured by observing their deflection in an electric field. After passing through the cylinders, the particles were collected in a trap cooled by liquid nitrogen. When the capillary valve was opened, the jet and the drops that were formed began to evaporate. Because of evaporative cooling, the particle temperature was re­duced and the evaporation diminished. In order to main­tain a good vacuum, the vapor from the evaporating particles was collected by a liquid-nitrogen-cooled trap which surrounded the region containing the capillary.

In order to measure the velocity of the particles, the output of the oscillator was fed into a synchronous fre­quency reducer whose output was used to trigger an oscilloscope containing a variable-delay generator. The delay trigger of the oscilloscope was then used to drive a stroboscope. The velocity of the particles was found by measuring the distance that the pattern of the drops moved for a certain change in the delay time under illumination of the strobe light.

outercylinderJ::::::: : :::::: magnet

cold trap

centrol cylinder

l : : : : : : : : : :(: : : :

FIG. 2. Experimental setup.

oscillator

!leloctromeChoniCOI transdJcer

g;: partICle geroenJ1o<

coIdt~

[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 129.174.21.5

On: Mon, 22 Dec 2014 04:11:24

1178 T.C. Anestos and C.D. Hendricks: Small macroscopic particles into plasmas 1178

0.3

0.2

E u

c: ,2 U .!! -Q)

0.1 0

100 200 300 400 500 Voltage (volts)

FIG. 3. Deflection of particles as function of magnetron voltage.

600

When the plasma was present, the beam was deflected away from the central cylinder (the cathode), w:hich indicated that the particle was negatively charged. Figure 3 shows the deflection as a function of the voltage difference between the coaxial cylinders. The charge on the particle is given by

ne-~ rln(ra/rj)L2y (10) - 8 1TptrV2V

where p= O. 79 X 103 kg/m is the density of alcohol, a =12.5x10-6 m is the radius of the particle, v=18 m/ sec is the velocity of the particle, r/rc = 30 is the ratio of the radii of the outer to the central cylinder, L = O. 24 m is the distance the particles travel in the electric field, r = 0.5 x 10-2 m is the distance of the particle traj ectory from the central cylinder, y is the deflection of the traj ectory from the traj ectory of an uncharged particle, and V is the potential difference between the coaxial cylinders.

From Eq. (10) and Fig. 3 the charge of the particles is found to be 6 x10-15 C. Then, ecp/k= 50 000 oK.

Substituting this value for ecp/k in Eq. (9) and taking T j = 300 OK, we obtain

Te = 19500 OK.

The value for Te obtained in this way was compared with the value obtained with a cylindrical Langmuir probe. From the slope of the curve of current vs probe potential, Te was found to be 16500 OK.

The electron temperature of a helium plasma was also measured and found to be 150000 GK. Probe mea­surements gave the value of 140000 OK.

J. Appl. Phys., Vol. 45, No.3, March 1974

The effect of the magnetic field present in the cylin­drical space is to lower the electron current on the particle. However, when the radius of the particle is smaller than the Larmor radius of the electrons, the effect on the electron current is negligible. In the pres­ent experiment the Larmor radius of the electrons was about 260 /l, which is much larger than the radius of the particles. As a result the electron current on the particles was not affected by the magnetic field. This points out the advantage of using very small macro­scopic particles in plasmas where high magnetic fields exist.

The most Significant advantage of the inj ection of small macroscopic particles in plasmas occurs in the case of high-density and high-temperature plasmas. The particles are in the plasma a very short period of time, of the order of 10-2 sec; therefore, they would not lose a significant amount of mass as a result of evapo­ration, while an ordinary probe held for a long time in this plasma may actually melt. In the case of a very hot plasma, where the particles would lose some mass, measurements of the mass loss could provide informa­tion about the plasma densities. In order to avoid con­tamination of the plasma, the particles must be of the same element as the ions of the plasma. It was possible to successfully generate liquid oxygen particles directly into the vacuum. In the case of elements that exist as liquids within only a very small range of temperatures­e.g., argon and deuterium-the generation of particles in vacuum presents some difficulties because the jet may freeze owing to evaporation before it breaks into drops. In this case, the breaking of the jet into drops can be accomplished at pressures near the triple point of the phase diagram, and then the drops can be injected into the vacuum through a differentially pumped system. Once in the high-vacuum portion of the system, the 'drops freeze by evaporative COOling into solid spherical pellets. The total loss of mass by evaporation during the cooling process is only a few percent.

ACKNOWLEDGMENTS

The authors are grateful to Christofer Foster and Kam Fook Yeung for their valuable suggestions in this work. This work was supported by Grants No. AF-AFOSR 68-1508 and No. AFOSR 73-2481 from the U. S. Air Force Office of Scientific Research and by the Physical Electronics Industrial Mfiliates Program.

1S. L. Gralnick, Ph. D. thesis (Columbia University 1972) (unpublished) . '

2C. T. Chang, A.H. Silleson, and F. Foster, Note on the Pellet-Plasma Interaction Problem and Possible Preliminary

3 Experimental Investigations (Danish AEC, Riso, 1971). H. Mott-Smith and Irving Langmuir, Phys. Rev. 28 727 (1926). '

4R.T. Bettinger and E.H. Walker, Phys. Fluids 8, 748 (1965). 5J.M. Schneider, N.R. Lindblad, C.D. Hendricks, and J.M. Crowley, J. Appl. Phys. 38, 2599 (1967).

6N.R. Lindhlad and J. M. Schneider, J. Sci. Instrum. 42, 635 (1965).

[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 129.174.21.5

On: Mon, 22 Dec 2014 04:11:24