NASA TECHNICAL NOTE ASA TN D-7167

v ,ENERGY DISTRIBUTION FUNCTIONSOF KILOVOLT IONS PARALLEL ANDPERPENDICULAR TO THE MAGNETIC FIEOF A MODIFIED PENNING DISCHARGE

by J. Reece Roth

Lewis Research Center

Cleveland, Ohio 44135

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION • WASHINGTON, D. C. • FEBRUARY 1973

https://ntrs.nasa.gov/search.jsp?R=19730007963 2018-06-08T15:54:44+00:00Z

1. Report No. 2. Government Accession No,

NASA TN D-71674. Title and Subtitle ENERGY DISTRIBUTION FUNCTIONS OF KILO-

VOLT IONS PARALLEL AND PERPENDICULAR TO THEMAGNETIC FIELD OF A MODIFIED PENNING DISCHARGE

7. Author(s)

J. Reece Roth

9. Performing Organization Name and Address

Lewis Research CenterNational Aeronautics and Space AdministrationCleveland, Ohio 44135

12. Sponsoring Agency Name and Address

National Aeronautics and Space AdministrationWashington, D.C. 20546

3. Recipient's Catalog No.

5. Report DateFebruary 1973

6. Performing Organization Code

8. Performing Organization Report No.

E-7181

10. Work Unit No.

503-1011. Contract or Grant No.

13. Type of Report and Period Covered

Technical Note14. Sponsoring Agency Code

15. Supplementary Notes

16. Abstract ,

The distribution function of ion energy parallel to the magnetic field of a modified Penning dis-charge has been measured with a retarding potential energy analyzer. These ions escapedthrough one of the throats of the magnetic mirror geometry. Simultaneous measurements ofthe ion energy distribution function perpendicular to the magnetic field have been made with acharge-exchange neutral detector. The ion energy distribution functions are approximatelyMaxwellian, and the parallel and perpendicular kinetic temperatures are equal within experi-mental error. These results suggest that turbulent processes previously observed in this dis-charge Maxwellianize the velocity distribution along a radius in velocity space and cause anisotropic energy distribution. The kinetic temperatures observed are of the order of kilovolts,and the tails of the ion energy distribution functions are Maxwellian for up to a factor of7 e-folds in energy. When the distributions depart from Maxwellian, they are enhanced above

1 (\ O

the Maxwellian tail. Above densities of about 10 particles/cm , this enhancement appearsto be the result of a second higher temperature Maxwellian distribution. At these high ener-gies, only the ions perpendicular to the magnetic field lines'were investigated. - • •

17. Key Words (Suggested by Author(sl)

Plasma heating Ion heatingIon energy distribution Neutral detectorIon kinetic temperature

19. Security Oassif. (of this report)

Unclassified

18. Distribution Statement

Unclassified - unlimited

20. Security Classif. (of this page) 21. No. o

Unclassified 1(

f Pages 22. Price*

3 $3.00

*For sale by the National Technical Information Service, Springfield, Virginia 22151

ENERGY DISTRIBUTION FUNCTIONS OF KILOVOLT IONS PARALLEL

AND PERPENDICULAR TO THE MAGNETIC FIELD OF

A MODIFIED PENNING DISCHARGE

by J. Reece Roth

Lewis Research Center

SUMMARY

The distribution function of ion energy parallel to the magnetic field of a modifiedPenning discharge has been measured with a retarding potential energy analyzer. Theseions escaped through one of the throats of the magnetic mirror geometry. Simultaneousmeasurements of the ion energy distribution function perpendicular to the magnetic fieldhave been made with a charge-exchange neutral detector. The ion energy distributionfunctions are approximately Maxwellian, and the parallel and perpendicular kinetic tem-peratures are equal within experimental error. These results suggest that turbulentprocesses previously observed in this discharge Maxwellianize the velocity distributionalong a radius in velocity space and cause an isotropic energy distribution. The kinetictemperatures observed are of the order of kilovolts, and the tails of the ion energy dis-tribution functions are Maxwellian for up to a factor of 7 e-folds in energy. When thedistributions depart from Maxwellian, they are enhanced above the Maxwellian tail.Above densities of about 10 particles per cubic centimeter, this enhancement appearsto be the result of a second, higher temperature Maxwellian distribution. At these highparticle energies, only the ions perpendicular to the magnetic field lines were investi-gated.

INTRODUCTION

Previous investigations of a modified Penning discharge (ref. 1) revealed ions withapproximately Maxwellian velocity distributions and kilovolt kinetic temperatures. Thediagnostic instrument used to measure the energy distribution of ions parallel to themagnetic field lines was a retarding potential analyzer, located outside one of the mag-

netic mirrors. The data reduction procedures and experimental results from an exten-sive series of measurements with the retarding potential energy analyzer have beenreported elsewhere (ref. 2).

In view of the possible application of the modified Penning discharge to a steady-state plasma heating scheme for fusion research, it is desirable to confirm independent-ly the high ion kinetic temperatures and Maxwellian velocity distribution observed in theions lost along the magnetic-field lines. This report describes an investigation in whichthe parallel and perpendicular ion energy distribution functions were simultaneouslymeasured for 163 experimental runs taken under a range of operating conditions. Suchsimultaneous measurements have not been reported in the literature of Penning dis-charges, although Konstantinov, Myskin, Sorokin, and Tsel'nik (ref. 3) have measuredthe energy of charge-exchange neutrals from the midplane of a modified Penning dis-charge. In the investigation described in this report, a charge-exchange neutral detec-tor was used to measure the perpendicular ion energy, while simultaneous observationsof the parallel ion energy were made with the retarding potential energy analyzer.

Characteristics of Modified Penning Discharge

The operating characteristics of the discharge have been described in references1 and 4; a detailed description of the superconducting magnet facility in which the dis-charge is operated is described in reference 5; and some of the physical processes re-sponsible for ion heating are discussed in reference 6. An isometric cutaway drawing ofthe experimental configuration is shown in figure 1. The plasma is approximately15 centimeters in diameter at the midplane. The magnetic field consists of a magneticmirror with a 2. 62:1 mirror ratio generated by two superconducting coils, the Dewarsof which are approximately 18 centimeters in diameter at the magnetic mirror throats.The magnet system shown in figure 1 is located in a vacuum tank 1 meter in diameterand approximately 2 meters long and gives very good experimental and visual access tothe experimental volume. The parallel Dewars on either side of the experimental vol-ume are at liquid-nitrogen temperature. The anode ring is operated at positive poten-tials up to 35 kilovolts with respect to the walls of the vacuum tank, and the electricalcircuit to the power supply is completed by ions which impinge on the grounded tankwalls.

The experimental investigation consisted of 163 runs taken with deuterium gas. Themaximum value of the magnetic field was 1 tesla at the magnetic mirror throats and0. 38 tesla at the midplane, in the vicinity of the anode rings. From previous measure-ments taken with a Langmuir probe at the throat of the mirror (ref. 6), the electrontemperature is known to be approximately 50 eV, within a factor of 2, in this plasma.

-Superconductingmagnet dewars(ground potential)—7

Charge-exchangeneutral detector

18-cmworkingdiameter

^—Retarding potentialenergy analyzer

CD-11379-25

Figure 1. - Isometric cutaway drawing of modified Penning discharge and superconducting magnetic mirror facility.Approximate locations of retarding potential energy analyzer and of fast neutral energy analyzer are shownschematically.

This is as much as an order of magnitude below the ion temperature at the same operat-ing conditions. Any atomic deuterium generated in the plasma volume has ample oppor-tunity to recombine on the walls before it can return to the experimental volume, as aresult of the long mean free paths for binary collision processes. Because of the ratherlarge vacuum-tank wall area and the cold liquid-nitrogen surfaces on either side of theplasma volume, it is unlikely that a significant population of atomic deuterium can existin the plasma. For this reason it was assumed that the neutral background gas consistedof molecular deuterium gas. The principal ionized species within the plasma was takento be ionized deuterium atoms D+. It is believed that D+ dominated the plasma be-cause investigation of the spectrum of electrostatic potential fluctuations yielded a peakat the ion cyclotron frequency of D+ (when such a peak could be observed), and peakswere absent or much fainter by comparison at the ion cyclotron frequency appropriateto ionized molecular deuterium Dg.

The 163 experimental runs spanned a range of the positive anode voltage from 5 to35 kilovolts and neutral background pressures pQ from 3.9x10 to 12. 0x10 torr,where the neutral deuterium pressure has been corrected for the gage factor of thisapparatus. It was estimated from previous work (ref. 6) that the ion density at the mid-plane of the modified Penning discharge ranged f:tides per cubic centimeter in this investigation.

9 10plane of the modified Penning discharge ranged from approximately 10 to 6x10 par-

Diagnostic Instruments

The ion energy distribution function was measured by two nonperturbing diagnostictechniques, one parallel to the magnetic-fie Id lines, and the other perpendicular to themagnetic-field lines. In figure 2(a) is a schematic drawing of the retarding potentialenergy analyzer used to measure the parallel distribution function of ions leaving theplasma through the magnetic mirror throat. The analyzer was located approximately20 centimeters outside the magnetic mirror throat and 10 centimeters from the magneticaxis. The analyzer was parallel to the local magnetic-fie Id line and measured the paral-lel component of the ion energy. The raw data, taken on an X, Y-recorder, representedan integrated ion energy distribution function. A computer program determined, byiteration, the integrated Maxwellian distribution which best fit the raw data, in the senseof minimizing the mean square error between the logarithms of the best-fitting distri-bution and of the raw data. Using the logarithm of the value of the data point rather thanthe actual value of the data point tended to give approximately equal weight to all portionsof the data curves. By comparing the best-fitting computer solution to the raw data,one may assess the extent to which the raw data are Maxwellian by observing the extentto which the best-fitting curve is also a good fit. The principal source of error for thisapplication of the retarding potential energy analyzer is in the iterative procedure used

4

Magnet dewar

Y-axie

X, Y-reoorder

(a) Retarding potential energy analyzer, located approximately 4 centimeters fromplasma axis and 20 centimeters outside magnetic mirror throat.

Electrostaticdeflectorplates v^

{-Gas cell (nitrogen)

-Slits

-Ion spoke

PhotomultiplierLJ detector CD-11374-25

(b) Schematic drawing of charge-exchange neutral detector. Line of sight of the detectorwas tangent to sheath between plasma and anode ring approximately 6 centimeters belowmagnetic axis.

Figure 2. -Apparatus for measurement of parallel and perpendicular ion energydistribution functions.

to reduce the data, which sometimes does not converge to the proper kinetic tempera-ture. (This was determined by obtaining a best fit to "pseudodata, " an integrated Max-wellian of specified kinetic temperature.) These convergence problems give rise toerrors in the parallel-ion kinetic temperature which may be as high as 20 percent. Theanalytical theory, error analysis, and experimental application of the retarding poten-tial energy analyzer are discussed in reference 2.

The charge-exchange neutral detector used in these investigations is a geometricduplicate of that developed at Fontenay-aux-Roses (ref. 7). The particle detector elec-tronic system was developed at the NASA Lewis Research Center. A schematic showingthis instrument and its location with respect to the plasma is presented in figure 2(b).The retarding potential energy analyzer and the neutral detector were positioned tosample the anode sheath, approximately 1 centimeter from the inner circumference ofthe anode ring. Fast ions in the sheath between the plasma and the anode ring chargeexchange on the background of neutral molecular deuterium gas, and the resulting fastdeuterium atoms then move along straight lines to the walls of the vacuum vessel. Inthe neutral detector, some of the fast neutrals pass through a series of slits and arereionized by a nitrogen gas cell, which is maintained at pressures of approximately0.10 torr. The reionized fast particles then pass through additional focusing slits intoa set of 90° electrostatic deflector plates. The energy of the ions which may passthrough the 90° deflector plates is determined by the potential applied across them. Bychanging the voltage applied between the deflector plates, one may sweep out the energydistribution function of the reionized particles. The ions are passed through a secondseries of slits and impinge on a photomultiplier detector, which counts individual par-ticles.

The particle flux at the photomultiplier is only indirectly related to the ion distribu-tion function inside the confined plasma. To obtain the original ion distribution function,one must correct for the charge-exchange process of atomic deuterium ions on molecu-lar deuterium,

D+ + D2 - D£ + D°

One must also correct for the reionization cross section in the nitrogen gas cell and forthe energy resolution of the electrostatic analyzer. The flux I(V) of individual particlesreaching the photomultiplier (see the appendix) may be written

KV) = C0ninoax(V)Vif(V)k(V)Ga(V) (1)

where V is the ion energy in electron volts, GO is a geometrical and dimensional con-stant, f(V) is the desired ion energy distribution, k(V) is the reionization probability of

atomic deuterium in a nitrogen gas cell, and G (V) is a correction for the energy reso-lution of the analyzer and results from the fact that the relative energy resolution dV/Vis independent of energy. Thus, the energy resolution involves correction by a factor

Ga(V) ~ V (2)

The factor njnQ^CVjv.^ is the number of charge-exchange reactions per cubic centime-ter per second in the volume sampled by the analyzer, n. and nQ are the ion and neu-tral number density, respectively, and v^ is the deuterium ion velocity. The charge-exchange cross section a (V) is available in reference 8 and is known from 70 eV ^ V

X.

^ 200 keV. The correction factor k(V) for the nitrogen gas cell is known for energiesover the range 2 < V ^ 100 keV and is

k(V) ~ V0' 56 (3)

over this range (refs. 7 and 8).One may convert the raw data for I(V) to the distribution function of ion energy in

the plasma f(V) by using equations (1) to (3) to obtain

CjKV)f ( V ) = i (4)

V2'06ax(V)

where C^ is a constant for the apparatus. The ion energy distribution function ob-tained from equation (4) was used as input to a computer program which obtained aMaxwellian distribution with a least-squares best fit to the experimentally determinedion energy distribution f(V). Because the correction factor k(V) was not known fornitrogen gas below 2 kilovolts, raw data below 2 kilovolts were not utilized in obtainingthe best-fitting Maxwellian distribution. The principal error in applying the neutraldetector arose from establishing the zero level and rounding off errors in reading theraw data. These errors, combined with uncertainties in the charge-exchange crosssections, may have introduced an error of as much as 10 percent in determining theperpendicular ion kinetic temperature.

EXPERIMENTAL RESULTS

In figure 3 is shown a characteristic example of data which were taken simultane-ously with the retarding potential energy analyzer and the charge-exchange neutral de-tector. The anode voltage was 8 kilovolts, and the neutral background gas pressure was

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Figure 3. - Example of parallel and perpendicularMaxwellian ion energy distribution functionsmeasured with instruments shown in figure 2.Anode voltage, 8 kilovoltsf deuterium gas pressure,5.2x10-5 torr.

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Figure 4. - Example of parallel and perpendicularMaxwellian ion energy distribution functionsmeasured with instruments shown in figure 2.Anode voltage, 35kilovolts; deuterium gas pressure,4.3x10-5 torr.

5.2x10"^ torr of deuterium. Figure 3(a) is the energy distribution function measuredwith the charge-exchange neutral detector, corrected with equation (4), and plotted as afunction of energy on a semilogarithmic graph. The corrected raw data are indicatedby the round symbols, and the Maxwellian distribution which best fits these raw data isindicated by the triangular symbols. In figure 3(b) is shown the integrated energy dis-tribution function measured with the retarding potential energy analyzer. The round

8

symbols are the corrected raw data, and the triangular symbols are the best-fittingintegrated Maxwellian distribution. Figure 3(a) gives a perpendicular component of theion kinetic temperature, Vj_ = 620 eV, and figure 3(b) a best-fitting parallel kinetic tem-perature, V|| = 559 eV. It is characteristic in figure 3 that both the parallel and perpen-dicular ion energy distribution functions are approximately Maxwellian, that the Max-wellian tail of the neutral detector data extends over approximately seven e-foldinglengths in energy, and that the parallel and perpendicular ion energies are approximate-ly equal within the scatter in the data of the two diagnostic methods employed.

In figure 4 is a second example of the perpendicular and parallel ion energy spectra,under conditions which yielded kinetic temperatures of nearly 2 kilovolts. The operatingconditions were an anode voltage of 35 kilovolts, and a neutral background gas pressureof 4.3x10" torr of deuterium. In figure 4(a) is the neutral detector spectrum with abest-fitting perpendicular kinetic temperature of V± = 1942 eV. In figure 4(b) is theretarding potential data, with a best-fitting parallel kinetic temperature of Vj( = 1705 eV.The knee in the latter data indicates that the magnetic-field line on which the retardingpotential analyzer was located was floating at a positive potential of Vf = 2200 volts,an unusually high value for this experiment, but only 6 percent of the applied anodevoltage. Figures 3 and 4 are characteristic in that it was possible, because of instru-ment limitations, to take valid data at higher energies with the neutral detector thanwith the retarding potential energy analyzer.

Ion energy distributions analogous to those shown in figures 3 and 4 were obtainedfor all 163 runs. Temperatures obtained from the best-fitting Maxwellian distributionsare shown in figure 5. On the small number of occasions for which a two-temperatureMaxwellian distribution was observed with the neutral detector, the lower of the twokinetic temperatures was plotted in figure 5. On the abscissa is the kinetic temperaturederived from the parallel component of ion energy, measured with the retarding poten-tial energy analyzer. On the ordinate is the kinetic temperature derived from the per-pendicular component of ion energy measured with the charge-exchange neutral detector.There is approximate agreement of the parallel and perpendicular components of the ionkinetic temperature over the range of data taken.

The agreement of V, with V\\ and the degree of data spread may be estimated byfitting the data in figure 5 to the relation

V l=C2V . l <5>

and obtaining the median and relative standard deviation of Co. In figure 6, the cumu-lative probability of G£ for 163 runs is plotted on probability coordinates. The author'sbest estimate of the Gaussian distribution to the data is indicated by the straight line.

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Figure 5. - Paralles and perpendicular ion energiesdetermined from charge-exchange neutral detectorand retarding potential energy analyzer for 163experimental runs.

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Proportionality constant, C2

Figure 6. - Cumulative probability of observing value ofproportionality constant C2 from equation (5) forpopulation of 163 experimental runs. Median value ofC2, 1.04; standard deviation, 0.270; relative standarddeviation, 0.26.

The median value of C2, C2, is the intersection of the best-fitting straight line with the50 percent line,

= 1.04 (6)

which implies that the perpendicular energy is slightly higher than the parallel energy.The relative standard deviation of the data population, the horizontal distance betweenthe intersection of the best-fitting straight line with the median and the one standarddeviation lines, was approximately

6(C2)AC9=-^£- = 0.26 (7)

Thus, the parallel and perpendicular ion kinetic temperatures are equal to within theestimated experimental error. The parameter C2 was plotted as a function of the in-dependent variables (anode voltage and neutral gas pressure) for the 163 runs, and nosystematic trend of Cp was observed. The same physical process which is responsiblefor making C2 a fixed constant apparently operates over the entire range of parametersinvestigated.

Two general types of anomalous ion energy distributions were observed in the per-pendicular ion energy distribution function. Both were characterized by an increase of

10

the observed distribution function above the best-fitting Maxwellian value in the tail ofthe distribution. This enhancement of the Maxwellian tail assumed two forms. One ofthese was a two-temperature Maxwellian distribution, in which the Maxwellian tail wasdominated by a hotter component of lower density that gave the type of ion energy dis-tribution function illustrated in figure 7. Two-temperature distributions were observedonly at plasma densities above approximately 10 particles per cubic centimeter. Thistwo-temperature Maxwellian distribution apparently results from the analyzer samplingtwo separate regions with different ion kinetic temperatures.

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0 4 8 12 16 20Perpendicular ion energy, V^, kV

Figure 7. - Example of two-temperature Maxwelliandistribution observed with neutral detector at ionnumber densities above about 10 " per cubiccentimeter. Anode voltage 10 kilovolts; back-ground pressure, 7.8xlO"5'torr of deuterium gas.

Two-temperature Maxwellian distributions may also occur as a result of a popula-tion of hot impurities superimposed on the distribution function of the principal species.Such impurities, with each species having a distinct ion temperature, have been de-scribed by Stirling (ref. 9). This explanation" is unsatisfactory for the present experi-ment, however, since observation of the Penning discharge plasma with a bench spec-trometer revealed no detectable impurity lines. Ion energy distributions similar tofigure 7 have been reported by Artsimovich (ref. 10) in connection with the Tokamakseries of experiments. Artsimovich reported that two-temperature Maxwellian distri-

12butions occurred in the Tokamak at number densities below 10 particles per cubiccentimeter.

11

A second anomalous departure from the Maxwellian distribution was observed inapproximately a dozen cases, at higher neutral gas pressures. This departure is illus-trated in figure 8 and shows an ion energy distribution function with a bump on the Max-wellian tail at an energy which roughly corresponds to the voltage applied to the anodering. Such a distribution function may be due to physical processes in the weak plasmapenumbra which surrounds the modified Penning discharge.

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Figure 8. - Example of ion energy distribution function,measured with neutral detector, with a bump on theMaxweUiart tail. Anode voltage, 11 kilovolts-, back-ground pressure, 1. ZxlO"'' torr of deuterium gas.

DISCUSSION OF RESULTS

The present investigation has demonstrated generally good agreement between the •parallel and perpendicular kinetic temperatures observed with nonperturbing diagnosticsin a modified Penning discharge. These observations provide an independent confirma-tion of the results reported in reference 2, in -which a sophisticated data reduction pro-cedure was applied to raw data obtained from the modified Penning discharge with a re-tarding potential energy analyzer. The Maxwellian ion energy distributions observed inthe distribution functions parallel and perpendicular to the magnetic field are consistentwith a model in which the turbulent processes described in reference 4 tend to Maxwel-lianize the distribution function along a radius in velocity space in such a way that the ionenergy is also isotropic in velocity space..

The modified Penning discharge has been shown to be capable of generating asteady-state plasma of kilovolt ion energies with an energy distribution function that is

12

Maxwellian and virtually isotropic in velocity space. The modified Penning dischargemay therefore be of interest in controlled fusion experiments, particularly in thosetoroidal systems in which one desires to create an approximately isotropic distributionof hot ions.

R. P. G. Valckx and A. Bariaud of Fontenay-aux-Roses provided useful conversa-tions and assistance with the construction of the fast neutral energy analyzer.

Lewis Research Center,National Aeronautics and Space Administration,

Cleveland, Ohio, November 3, 1972,503-10.

13

APPENDIX - SYMBOLS

B magnetic-field strength, T

CQ constant appearing in eq. (1)

Ci constant appearing in eq. (4)

C2 constant appearing in eq. (5)

C2 median value of C2

AC2 defined by eq. (7)

6C2 standard deviation of C2

gr electric field strength, V/m

f (V) distribution function of ions in plasma

GA (V) correction for energy resolution of analyzer

I(V) particle flux

k(V) reionization probability in neutral gas cello

n. ion number density, particles/mo

nQ neutral particle density, particles/m

V ion energy, eV

V^ perpendicular component of ion energy

V1( parallel component of ion energy

vi ion velocity in plasma

a (V) charge-exchange cross section in plasmaX

14

REFERENCES

1. Roth, J. Reece: Modification of Penning Discharge Useful in Plasma Physics Ex-periments. Rev. Sci. Instr., vol. 37, no. 8, Aug. 1966, pp. 1100-1101.

2. Roth, J. Reece; and Clark, Marion: Analysis of Integrated Charged ParticleEnergy Spectra from Gridded Electrostatic Analyzers. Plasma Phys., vol. 11,no. 2, Feb. 1969, pp. 131-143.

3. Konstantinov, S. G.; Myskin, O. K.; Sorokin, A. F.; and Tsel'nik, F. A.: Low-Density Rotating Plasma in a Mirror. Soviet Phys.-Tech. Phys., vol. 16, no. 12,June 1972, pp. 2006-2010.

4. Roth, J. Reece: Experimental Study of Spectral Index, Mode Coupling, and EnergyCascading in a Turbulent, Hot-Ion Plasma. Phys. Fluids, vol. 14, no. 10,Oct. 1971, pp. 2193-2202.

5. Roth, J. Reece; Freeman, Donald C., Jr.; and Haid, David A.: SuperconductingMagnet Facility for Plasma Physics Research. Rev. Sci. Instr., vol. 36, no. 10,Oct. 1965, pp. 1481-1485.

6. Roth, J. Reece: Ion Heating Mechanism in a Modified Penning Discharge. NASATN D-6985, 1972.

7. Valckx, F. P. G.: Electrostatic Analyzer for the Detection of Fast Neutral Par-ticles. NASA TT F-11458, 1968.

8. Barnett, C. F.; Ray, J. A.; and Thompson, J. C.: Atomic and Molecular Colli-sion Cross Sections of Interest in Controlled Thermonuclear Research. Rep.ORNL-3113, Rev., Oak Ridge National Lab., Aug. 1964.

9. Stirling, W. L.: Lifetime of Hot-Ion Plasma in a Mirror Machine. Phys. Fluids,vol. 15, no. 4, Apr. 1972, pp. 688-692.

10. Artsimovich. L. A.: Tokamak Devices. Nucl. Fusion, vol. 12, no. 2, Mar. 1972,pp. 215-252.

NASA-Langley, 1973 25 E-7181 15

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