Abstract

Cyclic or chainlike inelastic collision processes are invoked as an hypothesis to explain the grossly non-thermodynamic properties of energetic carbon and gas-fed carbon arcs confined by magnetic fields. Elastic collisions between the fast electrons (v > v+ but EE+) and the hot ions appear to be only about one-tenth as efficient a process for heating the ions as the proposed multiple inelastic collision process, which we call excitation-heating. In addition, a revised treatment of the rate of energy transfer from hot carbon ions to the very cold electrons (v < v+) reduces the conventional ion cooling rate by a factor of about 6.

© 1966 Optical Society of America

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Corrections

J. Rand McNally, "Erratum: On the Possibility of Excitation Heating of Ions to High Temperatures," Appl. Opt. 5, 423-423 (1966)
https://www.osapublishing.org/ao/abstract.cfm?uri=ao-5-3-423

References

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  1. J. R. McNally, M. R. Skidmore, Appl. Opt. 2, 699 (1963). This paper gives a comprehensive review of earlier experiments. See also Optical Spectrometric Measurements of High Temperatures, P. J. Dickerman, ed. (Univ. of Chicago Press, 1961), pp. 70–94.
    [Crossref]
  2. J. R. McNally, M. R. Skidmore, J. Opt. Soc. Am. 47, 863 (1957); see also H. W. Drawin, Z. Phys. 174, 489 (1964).
    [Crossref]
  3. Strong laser action has been observed for λ 4880 Å of Ar+[E. I. Gordon, E. F. Labuda, W. B. Bridges, Appl. Phys. Letters 4, 178 (1964)]. One of us (JRM) has suggested the laser inversion mechanism may be due to2Ar++*(3p4 ¹D2)+1Ar+*(3p4 3d4D⁷/₂)→Ar++(3p4 ³P2)+Ar++(3p4 ³P0)+Ar+(3p4 4p ²D⁵/₂0)+0.005 eV; however, there appears to be compelling evidence that this is not a feasible interpretation (R. C. Miller, Bell Telephone Laboratories, private communication, April1965).
    [Crossref]
  4. J. R. McNally, M. R. Skidmore, ORNL-3652 (1964), pp. 74–77; ORNL-3564, pp. 67–71 (1963) available from authors.
  5. J. B. Hasted, R. A. Smith, Proc. Roy. Soc. (London) A235, 354 (1956).
  6. I. P. Flaks, E. S. Solovev, Zh. Tekhn. Fiz. 3, 577 (1958).
  7. The ionization of helium in the collision of two metastable helium atoms has an estimated σvof 5 × 10−8cm3/sec (A. R. Tynes, thesis, Oregon State Univ., Corvallis, Oregon, 1964), i.e., He* + He* → He2** → He2* + e(or He + He++ e). The cross section for triplet–triplet deactivation collisions has also been determined as 10−14cm2at 300°K [A. V. Phelps, J. P. Molnar, Phys. Rev. 89, 1202 (1953)]. P. L. Pakhomov, I. Y. Fugol, Dokl. Akad. Nauk SSSR 159, 59 (1964), report a rate one-half as large at 77°K as that of Phelps and Molnar at 300°K.
    [Crossref]
  8. E. Hinnov, J. G. Hirschberg, Phys. Rev. 125, 795 (1962), give a T−−4,5dependence for three-body recombinations.
    [Crossref]
  9. H. S. W. Massey, D. R. Bates, Rept. Progr. Phys. 9, 62 (1942); D. R. Bates, Atomic and Molecular Processes (Academic, New York, 1962).
    [Crossref]
  10. An auxiliary reaction is C2+*(3P0) + C2+*(3P0) → C2+(1P0) + C2+(1S) + 0.3 eV, which may enhance or quench the pumping cycle depending on whether or not a radiationless transition (1P0→ 1S) occurs during the collision.
  11. T. K. Fowler, M. Rankin, J. Nucl. Energy C4, 311 (1962).
  12. L. Spitzer, Physics of Fully Ionized Gases (Interscience, New York, 1962).
  13. H. N. Olsen, Phys. Rev. 124, 1703 (1961); see also G. Ecker, W. Kroll, Phys. Fluids 6, 62 (1963).
    [Crossref]
  14. See R. A. McFarland, Appl. Phys. Letters 5, 91 (1964).
    [Crossref]
  15. The charge-exchange reaction C2++ Ar → C++ Ar++ 8.6 eV has a cross section with a broad maximum of 2 × 10−15cm2at about 1-keV C2+giving σv~ 2.5 × 10−8cm3/sec (see ref. 5).

1964 (3)

Strong laser action has been observed for λ 4880 Å of Ar+[E. I. Gordon, E. F. Labuda, W. B. Bridges, Appl. Phys. Letters 4, 178 (1964)]. One of us (JRM) has suggested the laser inversion mechanism may be due to2Ar++*(3p4 ¹D2)+1Ar+*(3p4 3d4D⁷/₂)→Ar++(3p4 ³P2)+Ar++(3p4 ³P0)+Ar+(3p4 4p ²D⁵/₂0)+0.005 eV; however, there appears to be compelling evidence that this is not a feasible interpretation (R. C. Miller, Bell Telephone Laboratories, private communication, April1965).
[Crossref]

J. R. McNally, M. R. Skidmore, ORNL-3652 (1964), pp. 74–77; ORNL-3564, pp. 67–71 (1963) available from authors.

See R. A. McFarland, Appl. Phys. Letters 5, 91 (1964).
[Crossref]

1963 (1)

1962 (2)

E. Hinnov, J. G. Hirschberg, Phys. Rev. 125, 795 (1962), give a T−−4,5dependence for three-body recombinations.
[Crossref]

T. K. Fowler, M. Rankin, J. Nucl. Energy C4, 311 (1962).

1961 (1)

H. N. Olsen, Phys. Rev. 124, 1703 (1961); see also G. Ecker, W. Kroll, Phys. Fluids 6, 62 (1963).
[Crossref]

1958 (1)

I. P. Flaks, E. S. Solovev, Zh. Tekhn. Fiz. 3, 577 (1958).

1957 (1)

1956 (1)

J. B. Hasted, R. A. Smith, Proc. Roy. Soc. (London) A235, 354 (1956).

1942 (1)

H. S. W. Massey, D. R. Bates, Rept. Progr. Phys. 9, 62 (1942); D. R. Bates, Atomic and Molecular Processes (Academic, New York, 1962).
[Crossref]

Bates, D. R.

H. S. W. Massey, D. R. Bates, Rept. Progr. Phys. 9, 62 (1942); D. R. Bates, Atomic and Molecular Processes (Academic, New York, 1962).
[Crossref]

Bridges, W. B.

Strong laser action has been observed for λ 4880 Å of Ar+[E. I. Gordon, E. F. Labuda, W. B. Bridges, Appl. Phys. Letters 4, 178 (1964)]. One of us (JRM) has suggested the laser inversion mechanism may be due to2Ar++*(3p4 ¹D2)+1Ar+*(3p4 3d4D⁷/₂)→Ar++(3p4 ³P2)+Ar++(3p4 ³P0)+Ar+(3p4 4p ²D⁵/₂0)+0.005 eV; however, there appears to be compelling evidence that this is not a feasible interpretation (R. C. Miller, Bell Telephone Laboratories, private communication, April1965).
[Crossref]

Flaks, I. P.

I. P. Flaks, E. S. Solovev, Zh. Tekhn. Fiz. 3, 577 (1958).

Fowler, T. K.

T. K. Fowler, M. Rankin, J. Nucl. Energy C4, 311 (1962).

Gordon, E. I.

Strong laser action has been observed for λ 4880 Å of Ar+[E. I. Gordon, E. F. Labuda, W. B. Bridges, Appl. Phys. Letters 4, 178 (1964)]. One of us (JRM) has suggested the laser inversion mechanism may be due to2Ar++*(3p4 ¹D2)+1Ar+*(3p4 3d4D⁷/₂)→Ar++(3p4 ³P2)+Ar++(3p4 ³P0)+Ar+(3p4 4p ²D⁵/₂0)+0.005 eV; however, there appears to be compelling evidence that this is not a feasible interpretation (R. C. Miller, Bell Telephone Laboratories, private communication, April1965).
[Crossref]

Hasted, J. B.

J. B. Hasted, R. A. Smith, Proc. Roy. Soc. (London) A235, 354 (1956).

Hinnov, E.

E. Hinnov, J. G. Hirschberg, Phys. Rev. 125, 795 (1962), give a T−−4,5dependence for three-body recombinations.
[Crossref]

Hirschberg, J. G.

E. Hinnov, J. G. Hirschberg, Phys. Rev. 125, 795 (1962), give a T−−4,5dependence for three-body recombinations.
[Crossref]

Labuda, E. F.

Strong laser action has been observed for λ 4880 Å of Ar+[E. I. Gordon, E. F. Labuda, W. B. Bridges, Appl. Phys. Letters 4, 178 (1964)]. One of us (JRM) has suggested the laser inversion mechanism may be due to2Ar++*(3p4 ¹D2)+1Ar+*(3p4 3d4D⁷/₂)→Ar++(3p4 ³P2)+Ar++(3p4 ³P0)+Ar+(3p4 4p ²D⁵/₂0)+0.005 eV; however, there appears to be compelling evidence that this is not a feasible interpretation (R. C. Miller, Bell Telephone Laboratories, private communication, April1965).
[Crossref]

Massey, H. S. W.

H. S. W. Massey, D. R. Bates, Rept. Progr. Phys. 9, 62 (1942); D. R. Bates, Atomic and Molecular Processes (Academic, New York, 1962).
[Crossref]

McFarland, R. A.

See R. A. McFarland, Appl. Phys. Letters 5, 91 (1964).
[Crossref]

McNally, J. R.

Olsen, H. N.

H. N. Olsen, Phys. Rev. 124, 1703 (1961); see also G. Ecker, W. Kroll, Phys. Fluids 6, 62 (1963).
[Crossref]

Rankin, M.

T. K. Fowler, M. Rankin, J. Nucl. Energy C4, 311 (1962).

Skidmore, M. R.

Smith, R. A.

J. B. Hasted, R. A. Smith, Proc. Roy. Soc. (London) A235, 354 (1956).

Solovev, E. S.

I. P. Flaks, E. S. Solovev, Zh. Tekhn. Fiz. 3, 577 (1958).

Spitzer, L.

L. Spitzer, Physics of Fully Ionized Gases (Interscience, New York, 1962).

Tynes, A. R.

The ionization of helium in the collision of two metastable helium atoms has an estimated σvof 5 × 10−8cm3/sec (A. R. Tynes, thesis, Oregon State Univ., Corvallis, Oregon, 1964), i.e., He* + He* → He2** → He2* + e(or He + He++ e). The cross section for triplet–triplet deactivation collisions has also been determined as 10−14cm2at 300°K [A. V. Phelps, J. P. Molnar, Phys. Rev. 89, 1202 (1953)]. P. L. Pakhomov, I. Y. Fugol, Dokl. Akad. Nauk SSSR 159, 59 (1964), report a rate one-half as large at 77°K as that of Phelps and Molnar at 300°K.
[Crossref]

Appl. Opt. (1)

Appl. Phys. Letters (2)

Strong laser action has been observed for λ 4880 Å of Ar+[E. I. Gordon, E. F. Labuda, W. B. Bridges, Appl. Phys. Letters 4, 178 (1964)]. One of us (JRM) has suggested the laser inversion mechanism may be due to2Ar++*(3p4 ¹D2)+1Ar+*(3p4 3d4D⁷/₂)→Ar++(3p4 ³P2)+Ar++(3p4 ³P0)+Ar+(3p4 4p ²D⁵/₂0)+0.005 eV; however, there appears to be compelling evidence that this is not a feasible interpretation (R. C. Miller, Bell Telephone Laboratories, private communication, April1965).
[Crossref]

See R. A. McFarland, Appl. Phys. Letters 5, 91 (1964).
[Crossref]

J. Nucl. Energy (1)

T. K. Fowler, M. Rankin, J. Nucl. Energy C4, 311 (1962).

J. Opt. Soc. Am. (1)

ORNL-3652 (1)

J. R. McNally, M. R. Skidmore, ORNL-3652 (1964), pp. 74–77; ORNL-3564, pp. 67–71 (1963) available from authors.

Phys. Rev. (2)

E. Hinnov, J. G. Hirschberg, Phys. Rev. 125, 795 (1962), give a T−−4,5dependence for three-body recombinations.
[Crossref]

H. N. Olsen, Phys. Rev. 124, 1703 (1961); see also G. Ecker, W. Kroll, Phys. Fluids 6, 62 (1963).
[Crossref]

Proc. Roy. Soc. (London) (1)

J. B. Hasted, R. A. Smith, Proc. Roy. Soc. (London) A235, 354 (1956).

Rept. Progr. Phys. (1)

H. S. W. Massey, D. R. Bates, Rept. Progr. Phys. 9, 62 (1942); D. R. Bates, Atomic and Molecular Processes (Academic, New York, 1962).
[Crossref]

Zh. Tekhn. Fiz. (1)

I. P. Flaks, E. S. Solovev, Zh. Tekhn. Fiz. 3, 577 (1958).

Other (4)

The ionization of helium in the collision of two metastable helium atoms has an estimated σvof 5 × 10−8cm3/sec (A. R. Tynes, thesis, Oregon State Univ., Corvallis, Oregon, 1964), i.e., He* + He* → He2** → He2* + e(or He + He++ e). The cross section for triplet–triplet deactivation collisions has also been determined as 10−14cm2at 300°K [A. V. Phelps, J. P. Molnar, Phys. Rev. 89, 1202 (1953)]. P. L. Pakhomov, I. Y. Fugol, Dokl. Akad. Nauk SSSR 159, 59 (1964), report a rate one-half as large at 77°K as that of Phelps and Molnar at 300°K.
[Crossref]

An auxiliary reaction is C2+*(3P0) + C2+*(3P0) → C2+(1P0) + C2+(1S) + 0.3 eV, which may enhance or quench the pumping cycle depending on whether or not a radiationless transition (1P0→ 1S) occurs during the collision.

L. Spitzer, Physics of Fully Ionized Gases (Interscience, New York, 1962).

The charge-exchange reaction C2++ Ar → C++ Ar++ 8.6 eV has a cross section with a broad maximum of 2 × 10−15cm2at about 1-keV C2+giving σv~ 2.5 × 10−8cm3/sec (see ref. 5).

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Figures (11)

Fig. 1
Fig. 1

Long solenoid facility used in study of magnetically confined arcs. Field of 8300 G requires 3000 A from two 1.75-MW dc generators.

Fig. 2
Fig. 2

Spectrogram of hydrogen and oxygen lines observed in magnetically confined, hydrogen arc with 3.4-m JAco grating spectrograph at high orders. Note slant-line effects due to doppler precessional velocity drift around arc column. Arc: 4.2 m long; 82 A; 178 V; 5.2 × 10−6 torr in mid-tank region; observation point 0.4 m from cathode.

Fig. 3
Fig. 3

Determination of electron-excitation temperature for magnetically confined lithium arc. I = measured line intensity with calibrated JAco 82000 spectrometer, λ = wavelength, f = oscillator strength of transition, g = statistical weight of upper state, E = energy in eV of upper state. Te ≃ −5040 (dE/d log I*), where I* = Iλ3/fgnupper. Conditions of lithium arc: 76 cm long, 100 A, 95 V, 25 cm from anode, 11,000 G.

Fig. 4
Fig. 4

Photograph of short section of energetic carbon arc confined by magnetic field. Ion temperatures up to 5,000,000°K and electron temperatures of order 40,000°K are measured spectroscopically and indicate a gross departure from thermodynamic equilibrium.

Fig. 5
Fig. 5

Doppler slant and broadening in spectra of C2+ in magnetically confined carbon arc: 135 A; 170 V; 5.45 m long; center manifold pressure = 4 × 10−6 torr; 8300, 5500, 8300, 5500, 8300 G (double-magnetic mirror); 5-cm. o.d. carbon anode; 1.27-cm o.d., 0.95-cm i.d. carbon cathode.

Fig. 6
Fig. 6

Observed line half-widths and associated ion temperatures of C2+ ions in 5.7-m carbon arc confined by magnetic field. Instrumental width ~ 0.3 Å. Ion temperature is leveling off at about 4.3 × 106°K in this arc. Conditions of arc: 1.9 cm o.d. hollow cathode (C); 5.1-cm o.d. solid anode (C).

Fig. 7
Fig. 7

Variation of doppler half-width and ion temperature as a function of the ratio of the resonance lines of C2+ and C3+ for various arc currents and several arc restarts. The trend suggests, but does not prove, that increased ion heating occurs with higher abundance of C2+. Increased gas-loading for the higher currents contributes some cooling effect. Conditions of arc: 7.6-cm diam C anode; 1.27-cm diam hollow cathode; P = 3 × 10−6 torr; arc length 5.8 m; observation 5.5 m from anode; 18 May 1965.

Fig. 8
Fig. 8

Example of determination of electron excitation temperature of carbon arc by two group average method (see Sec. VIII).

Fig. 9
Fig. 9

Selected low levels of C2+ to illustrate the effects of strongly allowed transitions in the preferential depopulation of certain levels in thin plasmas.

Fig. 10
Fig. 10

Schema to illustrate collision energetics of ion-heating process. If two metastable ions have sufficient collisional energy to overcome the potential barrier the exothermic reaction can occur at a critical internuclear separation. Approximately 45-eV kinetic energy is required if the critical distance is 1 Å.

Fig. 11
Fig. 11

Relative abundances of carbon ions vs electron temperature for ne = 1014 electrons/cm3 as determined by Saha relation.

Equations (15)

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C 2 + + e C 3 + + 2 e - 47.9 eV ( ionization ) ,
C 2 + + e C + + 24.4 eV ( recombination ) ,
C 3 + + C + C 2 + + C 2 + + 23.5 eV ( charge exchange resulting in ion heating ) ,
C hot + e cold C warm + e warm ( collisional heating of electrons ) .
C 2 + ( S 1 ) + e C 2 + * ( P 3 0 ) + e - 6.5 eV ( ion excitation ) ,
C 2 + * ( P 3 0 ) + C 2 + * ( P 3 0 ) C 2 + ( S 1 ) + C 2 + ( S 1 ) + 13.0 eV ( ion heating 10 ) ,
C 2 + hot + e cold C 2 + warm + e warm ( ion cooling ) ,
Li + * ( P 3 0 ) + Li + * ( P 3 0 ) ( Li 2 3 + + e + Q ) Li + ( S 1 ) + Li 2 + ( S 2 ) + e + 42.4 eV .
d W d t = - 4 π ( Δ n - ) Z 2 e 4 m _ v + ln b max b min ,
τ ~ 2 b v + + ( 2 Z e 2 / b m ) ½ ,
d W d t = - 4 π ( Δ n - ) Z 2 e 4 m - v + { ln ( 1 + x ) 2 - 2 x 1 + x } ,
Δ E coll τ coll n * σ co 11 v + av ( 6.5 ) > 6 × 10 6
σ co 11 v + av > 3 × 10 - 8 cm 3 / sec for n * ~ 3 × 10 13 cm - 3 .
Δ E exc τ exc = f n - σ exc v - av ( 6.5 ) > 6 × 10 6
σ exc v - av > 3 × 10 - 8 cm 3 / sec ,

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