Skip to main content
SpringerLink
Log in

Teoria del trasporto elettronico in gas: processi di rilassamento

  • Published:
La Rivista del Nuovo Cimento (1978-1999) Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Bibliografia

  1. Andersen H. C., Oppenheim I., Shuler K. E. andWeiss G. H.,Exact conditions for the preservation of a canonical distribution in Markovian relaxation processes,J. Math. Phys.,5 (1964) 522–536.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  2. Andersen K. andShuler K. E.,On the relaxation of the hard-sphere Rayleigh and Lorentz gas,J. Chem. Phys.,40 (1964) 633–650.

    Article  MathSciNet  ADS  Google Scholar 

  3. Arsac A., Basquin L., Denisse J.-F., Delcroix J.-L. andSalmon J.,Calcul des valeurs propres de l’opérateur de collision élastique d’un gaz de Lorentz. Etude de quelques cas usuels. V,J. Phys. Rad.,19 (1958) 624–629.

    Article  MATH  Google Scholar 

  4. Barker J. A., Hoare M. R., Raval S. andRahman M.,Exact transform solution of the one-dimensional special Rayleigh problem,Can. J. Phys.,55 (1977) 916–928.

    Article  ADS  Google Scholar 

  5. Bayet M., Delcroix J.-L. andDenisse J.-F.,Théorie cinétique des plasmas homogènes faiblement ionisés, 1,J. Phys. Rad.,15 (1954) 795–803.

    Article  MathSciNet  MATH  Google Scholar 

  6. Bayet M., Delcrolx J.-L. andDenisse J.-F.,Théorie cinétique des plasmas homogènes faiblement ionisés, II,J Phys. Rad.,16 (1955) 274–280.

    Article  Google Scholar 

  7. Bayet M., Delcroix J.-L. andDenisse J.-F.,A propos de la théorie cinétique des plasmas homogénes,J. Phys. Rad.,16 (1955) 431.

    Article  MathSciNet  Google Scholar 

  8. Bayet M., Delcroix J.-L. andDenisse J.-F.,Théorie cinétique des plasmas homogènes faiblement ionisés, III.L’opérateur de collision dans le cas du gaz de Lorentz imparfait,J. Phys. Rad.,17 (1956) 923–930.

    Article  MathSciNet  Google Scholar 

  9. Bayet M., Delcrolx J.-L. andDenisse J.-F.,Théorie cinétique des plasmas homogènes faiblement ionisés, IV.Etude de l’èvolution de la partie isotrope de la fonction de distribution,J. Phys. Rad.,17 (1956) 1005–1009.

    Article  Google Scholar 

  10. Bayet M., Delcroix J.-L. andDenisse J. F.,Sur la résolution de l’équation de Boltzmann dans le cas d’un gaz de Lorentz imparfait Application aux gaz faiblement ionisés,Comptes Rendus (1957) 171–173.

  11. Blackmore R. andShizgal B.,Discrete-ordinate method of solution of Fokker-Planck equations with non-linear coefficients,Phys. Rev. A,31 (1985) 1855–1868.

    Article  ADS  Google Scholar 

  12. Blackmore R. andShizgal B.,A Solution of Kramers equation for the isomerization of n-butane in CCI4,J. Chem, Phys.,83 (1985) 2934–2941.

    Article  ADS  Google Scholar 

  13. Braglia G. L., de’Munari G. M. andMambriani G.,Thermalization times of low energy electrons in rare gases, CNEN RT/FI(65)61, Rome (1965).

  14. Braglia G. L., De’Munari G. M. andMambriani G.,A remark on thermalization time of low-energy electrons in rare gases,Nuovo Cimento,41 (1966) 96–98.

    Article  Google Scholar 

  15. Braglia G. L.,On the relaxation of a Maxwell-Lorentz gas in an electric field,Nuovo Cimento B,58 (1968) 352–360.

    Article  ADS  Google Scholar 

  16. Braglia G. L. andFerrari L.,On the derivation of the electron energy distribution in a gas in a field by Markoff’s method of solution of the random-flight problem,Lett. Nuovo Cimento,1 (1969) 595–600.

    Article  Google Scholar 

  17. Braglia G. L. andFerrari L.,«Stazionarization» of the velocity distribution function of electrons in a gas in an electric field,Nuovo Cimento B,67 (1970) 167–203;Erratum,2 (1971) 254.

    Article  ADS  Google Scholar 

  18. Braglia G. L. andFerrari L.,Time-dependent electron speed distribution functions in an electric field in a gas, I.«Stazionarization» in Ar, Krand Xe,Nuovo Cimento B,4 (1971a) 245–261.

    Article  ADS  Google Scholar 

  19. Braglia G. L. andFerrari L.,Time-dependent electron speed distribution functions in an electric field in a gas, II.Gas temperature effects,Nuovo Cimento B,4 (1971) 262–274.

    Article  ADS  Google Scholar 

  20. Braglia G. L. andFerrari L.,Fokker-Planck equation for the electron distribution in an electric field,Lett. Nuovo Cimento,4 (1972) 537–542.

    Article  Google Scholar 

  21. Braglia G. L. andFerrari L.,Rigorous analysis of the solution of the Boltzmann equation for a Maxwell-Lorentz gas in an electric field,Nuovo Cimento B,7 (1972) 119–136.

    Google Scholar 

  22. Braglia G. L. andFerrari L.,Solution of the Boltzmann equation for electrons in a gas in electric and magnetic fields, I.Steady-state solution,Physica,67 (1973) 249–273.

    Article  MathSciNet  ADS  Google Scholar 

  23. Braglia G. L. andFerrari L.,Solution of the Boltzmann equation for electrons in a gas in electric and magnetic fields, II.Time-dependent solution,Physica,67 (1973) 274–290.

    Article  MathSciNet  ADS  Google Scholar 

  24. Braglia G. L. andCaraffini G. L.,A note on the improvement of the Fokker-Planck equation for the energy distribution of charged particles in an electric field in a gas,Riv. Mat. Univ. Parma,3 (1974) 81–105.

    Google Scholar 

  25. Braglia G. L.,Time-dependent speed distribution of electrons in a field in a gas. Notes on the preservation of the «delta» form,Nuovo Cimento B,25 (1975) 479–494.

    Article  ADS  Google Scholar 

  26. Braglia G. L.,Remarks on the equation for the energy distribution of electrons in a gas in a field,Lett. Nuovo Cimento,16 (1976) 406–412.

    Article  ADS  Google Scholar 

  27. Braglia G. L.,The diffusion and drift of electrons in gases. A Monte-Carlo simulation,Physica C,92 (1977) 91–112.

    Article  Google Scholar 

  28. Braglia G. L. andCaraffini G. L.,Remarks on the equation for the energy relaxation of a Rayleigh gas,Riv. Mat. Univ. Parma,3 (1977) 285–300.

    Google Scholar 

  29. Braglia G. L., Caraffini G. L. andIori M.,Second-order theory of the electron drift velocity in a gas in a field,Lett. Nuovo Cimento,19 (1977) 193–200.

    Article  Google Scholar 

  30. Braglia G. L. andBaiocchi A.,The diffusion and drift of electrons in gases, II.A Monte-Carlo simulation in argon,Physica C,95 (1978) 227–243.

    Article  Google Scholar 

  31. Braglia G. L. andLowke J. J.,Comparison of Monte-Carlo and Boltzmann calculation of electron diffusion to absorbing electrodes,J. Phys. D,12 (1979) 1831–1838.

    Article  ADS  Google Scholar 

  32. Braglia G. L.,Theory of electron motion in gases, I.Stochastic theory of homogeneous system,Riv. Nuovo Cimento,3 (1980a) 1 e riferimenti citati. La teoria utilizzata in questo lavoro, riassunta in appendice A, è interamente sviluppata in questa monografia.

    Article  Google Scholar 

  33. Braglia G. L.,Motion of electrons and ions in a weakly ionized gas in a field, I.Foundations of the integral theory,Beitr. Plasmaphys.,20 (1980) 147–194, e riferimenti citati.

    Article  ADS  Google Scholar 

  34. Braglia G. L. andCaraffini G. L.,Second-order theory of electron diffusion perpendicular to an electric field in a gas,Lett. Nuovo Cimento,27 (1980) 145–151.

    Article  MathSciNet  ADS  Google Scholar 

  35. Braglia G. L.,On the accuracy of the iterative method for swarm transport coefficients,J. Chem. Phys.,74 (1981) 2990–2992.

    Article  ADS  Google Scholar 

  36. Braglia G. L.,On a computer simulation of electron swarm motion which competes with analytical methods,Lett. Nuovo Cimento,31 (1981) 183–188.

    Article  Google Scholar 

  37. Braglia G. L., Caraffini G. L. andDiligenti M.,A study of the relaxation of electron velocity distribution in gases,Nuovo Cimento B,62 (1981) 139–163.

    Article  ADS  Google Scholar 

  38. Braglia G. L.,Comment on «Electron diffusion under the influence of an electric field near absorbing boundaries», II,Phys. Rev. A,25 (1982) 1214–1217.

    Article  ADS  Google Scholar 

  39. Braglia G. L., Romanò L. andDiligenti M.,Monte-Carlo and Boltzmann calculations of electron transport in N2,Lett. Nuovo Cimento,35 (1982) 139–199.

    Article  Google Scholar 

  40. Braglia G. L., Romanò L. andDiligenti M.,Comment on «Comparative calculations of electron-swarm properties in N2 at moderate E/N values»,Phys. Rev. A,26 (1982) 3689–3694.

    Article  ADS  Google Scholar 

  41. Braglia G. L., Wilhelm J. andWinkler R.,Comparison between two approaches to the study of the collision dominated electron relaxation in weakly ionized plasmas under the action of an electric field,Ann. Phys. (Leipzig),39 (1982a) 338–348.

    Article  ADS  Google Scholar 

  42. Braglia G. L. andRomanò L.,Monte-Carlo and Boltzmann two-term calculations of electron transport in CO2,Lett. Nuovo Cimento,40 (1984) 513–518.

    Article  ADS  Google Scholar 

  43. Braglia G. L., Romanò L. andDiligenti M.,On the accuracy of experimental electron energy distributions in gases,Nuovo Cimento B,85 (1985) 193–207.

    Article  ADS  Google Scholar 

  44. Braglia G. L., Wilhelm J. andWinkler R.,Calculations of electron swarm properties in N2 at moderate values of E/N,Lett. Nuovo Cimento,44 (1985) 257–269.

    Article  Google Scholar 

  45. Braglia G. L., Wilhelm J. andWinkler R.,Multi-term solutions of Boltzmann’s equation for electrons in the real gases Ar, CH4 and CO2,Lett. Nuovo Cimento,44 (1985) 365–378.

    Article  Google Scholar 

  46. Braglia G. L., Winkler R. andWilhelm J.,Longitudinal- and transversal-diffusion coefficients for electrons in CH4, Arand CO2,Nuovo Cimento D,7 (1986) 681–699.

    Article  ADS  Google Scholar 

  47. Braglia G. L., Diligenti M., Wilhelm J. andWinkler R.,Multiterm calculations of electron energy distribution and transport coefficients in Arand Hg, I.Atoms at rest,Nuovo Cimento D,12 (1990) 257–276.

    Article  ADS  Google Scholar 

  48. Braglia G. L., Ricci G. L., Wilhelm J. andWinkler R.,Monte-Carlo and Boltzmann calculations of electron energy distributions in RFfields,Nuovo Cimento D,13 (1991a) 1235–1246.

    Article  ADS  Google Scholar 

  49. Braglia G. L. (A cura diSacchi C. A. andSona A.),Contributi alla fisica e modellistica delle sorgenti laser, riportato inLaser di potenza.Sorgenti e componenti ottici, Monografie Scientifiche del CNR, Roma (1991b).

    Google Scholar 

  50. Braglia G. L., Winkler R. andWilhelm J.,Monte-Carlo and Boltzmann calculations of the time-dependent velocity distribution of electrons in an electric field in a gas,Nuovo Cimento D,16 (1994a) 411–415.

    Article  ADS  Google Scholar 

  51. Braglia M., Winkler R. andWilhelm J.,On the relaxation of energetic electrons in plasmas,Contr. Plasma Phys.,31 (1991c) 463–481.

    Article  ADS  Google Scholar 

  52. Braglia M. andMinari P.,On the relaxation of the energy distribution function of light particles in heavy gases,Contr. Plasma Phys.,34 (1994b), 711–724.

    Article  ADS  Google Scholar 

  53. Brin A., Delcrok J.-L. andSalmon J.,Etude du refroidissement d’un gaz de particules chargées dans un plasma totalement ionisé, VI.J. Phys. Rad.,20 (1959) 529–534.

    Article  MATH  Google Scholar 

  54. Capitelli M. (Editor),Non-Equilibrium Vibrational Kinetics (Springer-Verlag, Berlin) 1986.

    Google Scholar 

  55. Carlile R. N.,Relaxation of the electron distribution function,IEEE Trans. Plasma Science,PS-12 (1984) 214–223.

    Article  ADS  Google Scholar 

  56. Cavalleri G.,Measurements of lateral diffusion coefficients and first Toumsend coefficients for electrons in helium by an electron-density sampling method,Phys. Rev.,179 (1969) 186–202.

    Article  ADS  Google Scholar 

  57. Chang J.-S., Hobson R. M., Laframboise J. G. andOgram G. L.,Theory of electron temperature relaxation in an afterglow plasma,J. Phys. B,11 (1978) 1675–1679.

    Article  ADS  Google Scholar 

  58. Cukier R. I. andShuler K. E.,On the microscopic conditions for linear macroscopic laws,J. Chem Phys.,57 (1972) 302–311.

    Article  ADS  Google Scholar 

  59. Cukier R. I. andHynes J. T.,On exponential time decay in relaxation,J. Chem. Phys.,64 (1976) 2674–2683.

    Article  ADS  Google Scholar 

  60. Davidenko V. A., Dolgoshein B. A., Somov S. V. andStarotel’tsev V. N.,Study of electron collisions in noble gases by means of a streamer,Sov. Phys. JETP,30 (1970) 49–53.

    ADS  Google Scholar 

  61. Dean A. G., Smith D. andAdams N. G.,Observations of electron temperature relaxation rates in rare gas afterglow plasmas,J. Phys. B,7 (1974) 644–656.

    Article  ADS  Google Scholar 

  62. Delcroix M. J.-L. andSalmon M. J.,Quelques propriétés particulières de l’opérateur de collision élastique de Boltzmann, VII,J. Phys. Rad.,20 (1959) 594.

    Article  MathSciNet  MATH  Google Scholar 

  63. Dolinsky A.,Numerical integration of kinetic equations,Phys. Fluids,8 (1965) 436–443.

    Article  ADS  Google Scholar 

  64. Drallos P. J. andWadehra J. M.,A novel algorithm for calculating the time evolution of the electron energy distribution function in gaseous discharges,J. Appl Phys.,63 (1988) 5601–5603.

    Article  ADS  Google Scholar 

  65. Drallos P. J. andWadehra J. M.,Exact time-dependent evolution of electron-velocity distribution functions in a gas using the Boltzmann equation,Phys. Rev. A,40 (1989) 1967–1975.

    Article  ADS  Google Scholar 

  66. Eaton C. F.,A transient solution of the Fokker-Planck equation,AIAA J.,2 (1964) 2033–2034.

    Article  ADS  Google Scholar 

  67. Eaton C. F. andHolway L. H. jr.,Energy loss to a cold background gas. I.Higher order corrections to the Fokker-Planck operator for a Lorentz gas, Phys. Rev.,143 (1966) 48–58.

    Article  ADS  Google Scholar 

  68. Eder O. J. andLackner T.,Systematic method for solving transport equations derived from master equations,Phys. Rev. A,28 (1983) 952–962.

    Article  MathSciNet  ADS  Google Scholar 

  69. Elliot C. J. andGreene A. E.,Electron energy distributions in e-Beam generated Xeand Arplasmas,J. Appl. Phys.,47 (1976) 2946–2953.

    Article  ADS  Google Scholar 

  70. Estocq E., Delouya G. andBretagne J.,Self-consistent modelling of X-ray preionized XeCl-laserdischarges,Appl. Phys. B,56 (1993) 209–221.

    Article  ADS  Google Scholar 

  71. Ferrari L.,On the velocity relaxation of a Rayleigh gas, I.Assumptions and approximations in the derivation of the usual kinetic equation,Physica A,115 (1982) 232–246.

    Article  ADS  Google Scholar 

  72. Ferrari L.,On the velocity relaxation of a Rayleigh gas, II.An investigation on reliability and accuracy of the usual kinetic equation,Physica A,127 (1984) 194–217.

    Article  ADS  Google Scholar 

  73. Ferrari L.,On the velocity relaxation of a Rayleigh gas, III.The relaxation of the heavy-particle velocity averages,Physica A,133 (1985) 103–119.

    Article  ADS  Google Scholar 

  74. Ferrari L.,On the velocity relaxation of a Rayleigh gas, IV.Remarks on the solution of the usual kinetic equation,Physica A,154 (1989) 271–288.

    Article  ADS  Google Scholar 

  75. Ferrari L.,Heavy ions in light gases in an electric field, II.Time-dependent solutions of the Fokker-Planck equation both in the absence and in the presence of a magnetic field,Physica A,163 (1990) 596–614.

    Article  ADS  Google Scholar 

  76. Ferreira C. M. andLeureiro J.,Electron excitation rates and transport parameters in high-frequency N2 discharges,J. Phys. D,22 (1989) 76–82.

    Article  ADS  Google Scholar 

  77. Frisch H. L.,Time lag in the thermalization of a fast ion in a plasma,Phys. Fluids,4 (1961) 1167–1171.

    Article  MathSciNet  ADS  Google Scholar 

  78. Garrett A. J. M.,Thermal relaxation and entropy for charged particles in a heat bath with fields,J. Phys. A,16 (1983) 1505–1516.

    Article  MathSciNet  ADS  Google Scholar 

  79. Garrett A. J. M.,The theory of thermal relaxation of light dilute particles in a heat bath:integral and differential elastic collision operators,Phys. Rep.,134 (1986) 195–271 e riferimenti citati.

    Article  MathSciNet  ADS  Google Scholar 

  80. Gee N. andFreeman G. R.,Thermal electron mobility and scattering in hexafluoroethane gas,J. Chem. Phys.,96 (1992) 6576–6579.

    Article  ADS  Google Scholar 

  81. Ghatak A. K.,Response of a Lorentzian gas to an a.c. pulse,Z. Phys.,226 (1969) 454–462.

    Article  ADS  Google Scholar 

  82. Ghatak A. K.,Response of a Lorentzian gas to an a.c. pulse. II,Z. Phys.,236 (1970) 245–249.

    Article  ADS  Google Scholar 

  83. Ghatak A. K., Chakravarti A. K. andRattan I.,Energy gap-temperature characteristics of ferroelectric triglycine selenate, J. Phys D, L29-L34 (1970).

  84. Gilardini A.,Low Energy Electron Collision in Gases (John Wiley & Sons, New York, N.Y.) 1972.

    Google Scholar 

  85. Goto N. andMakabe T.,Time-dependent electron swarm parameters in RFfields in CH4 and H2,J. Phys. D,23 (1990) 686–693.

    Article  ADS  Google Scholar 

  86. Gray A. H. jr.,Uniqueness of steady-state solutions to the Fokker-Planck equation, J. Math. Phys.,6 (1965) 644–647.

    Article  ADS  MathSciNet  Google Scholar 

  87. Gyorgy I. andFreeman G. R.,Ionization and electron thermalization distances in isomeric pentanes: Effects of molecular shape and density,J. Chem. Phys.,86 (1987) 681–687.

    Article  ADS  Google Scholar 

  88. Hansen L. K.,Comment on «Approach of electrons to equilibrium»,Phys. Fluids,9 (1966) 1618–1619.

    Article  ADS  Google Scholar 

  89. Hoare M. R.,The linear gas,Adv. Chem. Phys.,20 (1971) 135–214 e riferimenti citati.

    Google Scholar 

  90. Hoare M. R. andKaplinsky C. H.,Linear hard-sphere gas: Variational eigenvalue spectra of energy kernel,J. Chem. Phys.,52 (1970) 3336–3353.

    Article  MathSciNet  ADS  Google Scholar 

  91. Holway L. H. jr.,Time-varying weight functions and the convergence of polynomial expansions, Phys. Fluids,10 (1967) 35–48.

    Article  ADS  Google Scholar 

  92. Holway L. H. jr.,Temporal behavior of electron distributions in an electric field, Phys. Rev. Lett,28 (1972) 280–283.

    Article  ADS  Google Scholar 

  93. Holway L. H. jr.,High-frequency breakdown in ionic crystals, J. Appl. Phys.,45 (1974) 677–683.

    Article  ADS  Google Scholar 

  94. Huxley L. G. H. andCrompton R. W.,The Diffusion and Drift of Electrons in Gases (John Wiley & Sons, New York, N.Y.) 1974.

    Google Scholar 

  95. Hynes J. T.,Non-linear fluctuations in master equation systems, I.Velocity correlation function for the Rayleigh model,J. Chem Phys.,62 (1975) 2972–2981.

    Article  ADS  Google Scholar 

  96. Kahalas S. L. andKashian H. C.,On the approach of electrons to equilibrium,Phys. Fluids,2 (1959) 100–102.

    Article  ADS  MATH  Google Scholar 

  97. Kamal J. andGhatak A. K.,Response of a Lorentzian gas to an a.c. pulse, II,Z. Phys.,236 (1970) 245–249.

    Article  ADS  Google Scholar 

  98. Kitamori K., Tagashiea H. andSakai Y.,Relaxation process of the electron velocity distribution in neon,J. Phys. D,11 (1978) 283–292.

    Article  ADS  Google Scholar 

  99. Kitamori K., Tagashiea H. andSakai Y.,Development of electron avalanches in argon -an exact Boltzmann equation analysis,J. Phys. D,13 (1980) 535–550.

    Article  ADS  Google Scholar 

  100. Knierim K. D., Waldman M. andMason E. A.,Moment theory of electron thermalization in gases,J. Chem. Phys.,77 (1982) 943–950.

    Article  ADS  Google Scholar 

  101. Kociszewski A.,An information gain and open systems, I.Information gain solutions of a Fokker-Planck equation,Acta Phys. Polon. A,60 (1981) 291–301.

    MathSciNet  Google Scholar 

  102. Koura K.,Non-equilibrium electron velocity distribution and temperature in thermalization of low-energy electrons in molecular hydrogen,J. Chem. Phys.,79 (1983) 3367–3372.

    Article  ADS  Google Scholar 

  103. Koura K.,Isotope effects of H2 and D2 on electron thermalization in gases,J. Phys. Soc. Jpn.,53 (1984) 4192–4199.

    Article  ADS  Google Scholar 

  104. Koura K.,Monte-Carlo simulation of electron thermalization in gases, II.Subexcitation electrons in molecular hydrogen,J. Chem. Phys.,80 (1984) 5799–5805.

    Article  ADS  Google Scholar 

  105. Koura K.,Monte-Carlo simulation of electron thermalization in gases, III.Epithermal electrons in molecular nitrogen,J. Chem. Phys.,81 (1984) 303–308.

    Article  ADS  Google Scholar 

  106. Koura K.,Monte-Carlo simulation of electron thermalization in gases, TV. Subexcitation electrons in hard-sphere and Maxwell mode rare gases,J. Chem. Phys.,81 (1984) 4180–4181.

    Article  ADS  Google Scholar 

  107. Koura K.,Monte-Carlo simulation of electron thermalization in gases, V.Subexcitation electrons in rare gases,J. Chem. Phys.,82 (1985) 2566–2572.

    Article  ADS  Google Scholar 

  108. Koura K.,On the empirical equation for electron energy-loss rate in rare gases,J. Chem. Phys.,82 (1985) 4724–4726.

    Article  ADS  Google Scholar 

  109. Koura K.,Sensitivity of electron thermalization in rare gases to momentum-transfer cross section and impurities, TR-866T, National Aerospace Laboratory, Tokio, 1–10 (1985).

    Google Scholar 

  110. Koura K.,Monte-Carlo simulation of electron swarm in a model gas: transverse and longitudinal diffusion coefficients,J. Phys. Soc. Jpn.,55 (1986) 2500–2503.

    Article  ADS  Google Scholar 

  111. Koura K.,Monte-Carlo simulation of electron thermalization in gases, VI.Microwave conductivities of Heand Ar,J. Chem Phys.,84 (1986) 6227–6232; 86 (1987) 500.

    Article  ADS  Google Scholar 

  112. Koura K.,Monte-Carlo simulation of electron swarms in an argon-like gas,Aust. J. Phys.,40 (1987) 61–64.

    Article  ADS  Google Scholar 

  113. Koura K.,Monte-Carlo simulation of electron thermalization in gases, VII.Imaginary component of microwave conductivity of Ar,J. Chem. Phys.,87 (1987) 1248–1250.

    Article  ADS  Google Scholar 

  114. Koura K.,Monte-Carlo simulation of electron thermalization in gases, VIII.Thermalization distance and microwave conductivity in rare gases,J. Chem. Phys.,87 (1987) 6481–6487.

    Article  ADS  Google Scholar 

  115. Koura K.,Scaling rule for electron swarm in rare gases,J. Phys. Soc. Jpn.,56 (1987) 429–432.

    Article  ADS  Google Scholar 

  116. Krook M. andWu T. T.,Formation of Maxwellian tails,Phys. Rev. Lett,36 (1976) 1107–1109.

    Article  ADS  Google Scholar 

  117. Kumar K., Skullerud H. R. andRobson R. E.,Kinetic theory of charged particle swarms in neutral gases,Aust. J. Phys.,33 (1980) 343–448 e riferimenti citati.

    Article  MathSciNet  ADS  Google Scholar 

  118. Kumar K.,Short-time development of swarms-approach to hydrodynamic regime for charged particles in neutral gases,J. Phys. D,14 (1981) 2199–2208.

    Article  ADS  Google Scholar 

  119. Levine R. D. andBerrondo M.,An information theoretic derivation of the Fokker-Planck equation,Chem. Phys. Lett,47 (1977) 399–403.

    Article  MathSciNet  ADS  Google Scholar 

  120. Loffhagen D. andWinkler R.,A new nonstationary Boltzmann solver in self-consistent modelling of discharge pumped plasmas for excimer lasers,J. Comput. Phys.,112 (1994) 91–98.

    Article  ADS  MATH  Google Scholar 

  121. Loffhagen D., Winkler R. andBraglia G. L.,Non-stationary two-term and multi-term approximation of the velocity distribution in the temporal relaxation of plasma electrons (1995), in pubblicazione.

  122. Lyagushchenko R. I.,Relaxation of fast electrons in gases and semiconductors,Sov. Phys. JETP,36 (1973) 901–905.

    ADS  Google Scholar 

  123. Maeda K. andMakabe T.,Radiofrequency electron swarm transport in reactive gases and plasmas,Phys. Scr.,53 (1994) 61–69.

    Article  Google Scholar 

  124. McMahon D. R. A. andShizgal B.,Hot-electron zero-field mobility and diffusion in rare-gas moderators,Phys. Rev. A,31 (1985) 1894–1905. Sull’argomento si confronti il riferimento Bragliaet al. (1971a) non citato dagli autori.

    Article  ADS  Google Scholar 

  125. McMahon D. R. A., Ness K. andShizgal B.,Electric field dependence of transient electron longitudinal and tranverse diffusion coefficients in rare-gas moderators,J. Phys. B,19 (1986) 2759–2777.

    Article  ADS  Google Scholar 

  126. Makabe T. andGoto N.,The time behaviour of electron transport in RFfields in gases,J. Phys. D,21 (1988) 887–895.

    Article  ADS  Google Scholar 

  127. May R. M.,Relaxation of a fast ion in a plasma,Phys. Rev.,135 (1964) A1009-A1013.

    Article  ADS  MathSciNet  Google Scholar 

  128. May R. M.,Energy loss by fast test ions in a plasma,Aust. J. Phys.,22 (1969) 687–699.

    Article  ADS  Google Scholar 

  129. May R. M. andCramer N. F.,Energy loss of fast test ions in a plasma in a weak magnetic field,Phys. Lett. A,30 (1969) 10–11.

    Article  ADS  Google Scholar 

  130. May R. M. andCramer N. F.,Test ion energy loss in a plasma with a magnetic field,Phys. Fluids,13 (1970) 1766–1770.

    Article  ADS  Google Scholar 

  131. Mentzoni M. H. andRow R. V.,Rotational excitation and electron relaxation in nitrogen,Phys. Rev.,130 (1963) 2312–2316.

    Article  ADS  Google Scholar 

  132. Mentzoni M. H. andRao K. V. N.,Electron energy relaxation in oxygen,Phys. Rev. Lett,14 (1965) 779.

    Article  ADS  Google Scholar 

  133. Mentzoni M. H. andDonohoe J.,Energy relaxation for thermal electrons in CO,Can. J. Phys.,46 (1968) 1323–1330.

    Article  ADS  Google Scholar 

  134. Morgan W. L. andPenetrante B. M., ELENDIF:A time-dependent Boltzmann solver for partially ionized plasmas, Comput Phys. Commun.,58 (1990) 127–152.

    Article  ADS  Google Scholar 

  135. Mozumder A.,Electron thermalization in gases, I.Helium,J. Chem. Phys.,72 (1980) 1657–1664.

    Article  ADS  Google Scholar 

  136. Mozumder A.,Electron thermalization in gases, II.Neon, argon, krypton, and xenon,J. Chem. Phys.,72 (1980) 6289–6298.

    Article  ADS  Google Scholar 

  137. Mozumder A.,Electron thermalization in gases, III.Epithermal electron scavenging in rare gases,J. Chem. Phys.,74 (1981) 6911–6921.

    Article  ADS  Google Scholar 

  138. Mozumder A.,Electron thermalization in gases, IV.Relaxation time in molecluar hydrogen,J. Chem. Phys.,76 (1982) 3277–3284.

    Article  ADS  Google Scholar 

  139. Mozumder A.,Radiation induced conductivity in liquefied rare gases,J. Electrostatics,12 (1982) 45–57.

    Article  Google Scholar 

  140. Naidis G. V.,Relaxation of the electron energy distribution in an electric field,Sov. Phys. Tech. Phys.,22 (1977) 562–564.

    ADS  Google Scholar 

  141. Nakajima S., Seki Y. andIkuta N.,Boltzmann equation analyses of electrons in weakly ionized SiH4 gas under RFelectric field,Bull Fac. Engin.,27 (1990) 49–63.

    Google Scholar 

  142. Nakajima S., Okamoto T. andIkuta N.,Boltzmann equation analysis of position and time dependent velocity distribution of an electron swarm,Trans. IEE Jpn.,111 (1991) 139–146.

    Google Scholar 

  143. Nishigori T.,Memory function approach to non-linear deterministic systems: an exact linear equation,J. Math. Phys.,22 (1981) 2903–2909.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  144. Nishigori T. andSakai K.,Memory function approach to electron thermalization,J. Chem. Phys.,82 (1985) 2106–2109.

    Article  ADS  Google Scholar 

  145. Oppenheim I., Shuler K. E. andWeiss G. H.,Stochastic theory of multistate relaxation processes,Adv. Mol Relaxation Processes,1 (1967-68) 13–68 e riferimenti citati.

    Article  Google Scholar 

  146. Oser H., Shuler K. E. andWeiss G. H.,Relaxation of a Lorentz gas with a repulsive r -8 force law,J. Chem Phys.,41 (1964) 2661–2666.

    Article  MathSciNet  ADS  Google Scholar 

  147. Osipov D. I.,Conservation of the form of the Maxwellian distribution in a relaxing gas,AIAA J.,1 (1963) 261–262.

    Article  ADS  Google Scholar 

  148. Owedyk J. andKociszewski A.,On the Fokker-Planck equation with time-dependent drift and diffusion coefficients and its exponential solutions,Z. Phys. B,59 (1985) 69–74.

    Article  MathSciNet  ADS  Google Scholar 

  149. Pagani C. D.,Studio di alcune questioni concernenti l’equazione generalizzata di Fokker-Planck,Boll Un. Mat. Ital,6 (1970) 961–986.

    MathSciNet  MATH  Google Scholar 

  150. Piasecki J.,Time scales in the dynamics of the Lorentz electron gas,Am. J. Phys.,61 (1993) 718–722.

    Article  ADS  Google Scholar 

  151. Polman J.,Relaxation of the electron velocity distribution in a time-dependent weakly ionized plasma,Physica,54 (1971) 305–317.

    Article  ADS  Google Scholar 

  152. Provencher, S. W.,An eigenfunction expansion method for the analysis of exponential decay curves,J. Chem Phys.,64 (1976) 2772–2777.

    Article  ADS  Google Scholar 

  153. Ranganathan S. andShizgal B.,Transient microwave conductivity of electrons in helium,Chem. Phys. Lett.,134 (1987) 220–224.

    Article  ADS  Google Scholar 

  154. Rees H. D.,Time response of the high-field electron distribution function in GaAs,IBM J. Res. Develop.,13 (1969) 537–542.

    Article  Google Scholar 

  155. Rees H. D.,Calculating of distribution functions by exploiting the stability of the steady state,J. Phys. Chem. Solids,30 (1969) 643–655.

    Article  ADS  Google Scholar 

  156. Rees H. D.,The numerical analysis of semiclassical transport problems,J. Phys. C,3 (1970) 965–974.

    Article  ADS  Google Scholar 

  157. Rees H. D.,Numerical solution of electron motion in solids,J. Phys. C,5 (1972) 641–656.

    Article  ADS  Google Scholar 

  158. Rees H. D.,Computer simulation of semiconductor devices,J. Phys. C,6 (1973) 262–273.

    Article  ADS  Google Scholar 

  159. Reggiani L. (Editor),Hot-Electron Transport in Semiconductors (Spriger-Verlag, Berlin) (1985).

    Google Scholar 

  160. Robson R. E., Ness K. F., Sneddon G. E. andViehland L. A.,Comment on the discrete ordinate method in the kinetic theory of gases,J. Comput. Phys.,92 (1991) 213–229.

    Article  ADS  MATH  Google Scholar 

  161. Rockwood S. D.,Elastic and inelastic cross sections for electron-Hgscattering from Hgtransport data,Phys. Rev. A,8 (1973) 2348–2358.

    Article  ADS  Google Scholar 

  162. Sahni O. andJennings W. C.,Decay of electron average energy in the afterglow of low pressure pulsed nitrogen discharges,J. Phys. B,8 (1975) 1377–1391.

    Article  ADS  Google Scholar 

  163. Salmon J.,Théorie de la décharge haute fréquence dans les gaz aux basses pressions. Calcul de la fonction de distribution des électrons,J. Phys. Rad,16 (1955) 210–218.

    Article  Google Scholar 

  164. Salmon J.,Etude des plasmas en régime transitoire,J. Phys. Rad.,17 (1956) 931–933.

    Article  MathSciNet  MATH  Google Scholar 

  165. Shapiro C. S. andCorngold N.,Approach to equilibrium of a neutron gas,Phys. Rev. A,137 (1965) 1686–1696.

    Article  ADS  MATH  Google Scholar 

  166. Shizgal B.,Eigenvalues of the Lorentz Fokker-Planck equation,J. Chem. Phys.,70 (1979) 1948–1951.

    Article  ADS  Google Scholar 

  167. Shizgal B.,A Gaussian quadrature procedure for use in the solution of the Boltzmann equation and related problems,J. Coniput. Phys.,41 (1981) 309–328.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  168. Shizgal B.,Electron thermalization in gases,J. Chem. Phys.,78 (1983a) 5741–5744.

    Article  ADS  Google Scholar 

  169. Shizgal B.,Energy relaxation of electrons in helium,Chem. Phys. Lett,100 (1983b) 41–44.

    Article  ADS  Google Scholar 

  170. Shizgal B.,Discrete versus continuum relaxation modes of a hard sphere gas,Can. J. Phys.,62 (1984) 97–103.

    Article  ADS  Google Scholar 

  171. Shizgal B. andMcMahon D. R. A.,Electron distribution functions and thermalization times in inert gas moderators,J. Phys. Chem.,88 (1984) 4854–4862.

    Article  Google Scholar 

  172. Shizgal B. andMcMahon D. R. A.,Electric field dependence of transient electron transport properties in rare-gas moderators,Phys. Rev. A,32 (1985) 3669–3680.

    Article  ADS  Google Scholar 

  173. Shizgal B.,Transient electron mobilities in ethene and cyclopropane,Chem. Phys.,105 (1986) 325–332. Sull’argomento si confronti anche il riferimento Bragliaet al. (1971a), non citato dall’autore, nel quale fu messo in luce per la prima volta il fenomeno delia mobilità negativa di elettroni in Ar, Kr e Xe, un risultato qui attribuito impropriamente a McMahon e Shizgal (rif.McMahon et al. (1995)).

    Article  ADS  Google Scholar 

  174. Shizgal B. andNess K.,Thermalisation and annihilation of positrons in helium and neon,J. Phys. B,20 (1987) 847–865.

    Article  ADS  Google Scholar 

  175. Shizgal B.,The coupling of electron thermalisation and electron attachment; SF6 and CC14 in rare-gas moderators,J. Phys. B,21 (1988) 1699–1715.

    Article  ADS  Google Scholar 

  176. Shizgal B. andHatano Y.,Electron thermalization times for helium-krypton mixtures,J. Chem. Phys.,88 (1988) 5980–5982.

    Article  ADS  Google Scholar 

  177. Shizgal B., McMahon D. R. A. andViehland L. A.,Thermalization of electrons in gases,Radiat. Phys. Chem.,34 (1989) 35–50 e riferimenti citati.

    ADS  Google Scholar 

  178. Shizgal B.,Relaxation constants in electron thermalization: comparison of WKBand SWKBeigenvalues with exact results,Can. J. Phys.,68 (1990) 1213–1219. Sull’argomento trattato in questo lavoro e nel riferimento successivo si confrontino anche i riferimentiBraglia et al. (1970), (1971a) e (1981) non citati dagli autori.

    Article  ADS  Google Scholar 

  179. Shizgal B. andDemeio L.,Comparison of WKB (Wentzel-Kramers-Brillouin) and SWKBsolutions of Fokker-Planck equations with exact results;application to electron thermalization,Can. J. Phys.,69 (1991) 712–719.

    Article  ADS  Google Scholar 

  180. Shuler K. E., Weiss G. H. andAndersen K.,Studies in non-equilibrium rate processes, V.The relaxation of moments derived from a master equation,J. Math. Phys.,3 (1962) 550–556.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  181. Skullerud H. R. andKuhn S.,On the calculation of ion and electron swarm properties by path integral methods,J. Phys. D,16 (1983) 1225–1234.

    Article  ADS  Google Scholar 

  182. Sowada U. andWarman J. M.,Hot electron thermalisation in fluid argon—The effect of the Ramsauer-minimum,J. Electrost,12 (1982) 37–43.

    Article  Google Scholar 

  183. Stenflo L.,Time-dependent phenomena for a weakly ionized plasma in an external electric field,Ark. Fys.,38 (1968) 267–276.

    MATH  Google Scholar 

  184. Suzuki M., Ruan(gen) J. andKubota S.,Time dependence of the ricombination luminescence from high-pressure argon, krypton and xenon excited by alpha particles,Nucl. Instrum. Methods,192 (1982) 565–574.

    Article  ADS  Google Scholar 

  185. Takahashi T., Ruan(gen) J., Kubota S. andShiraishi F.,Time delay of recombination luminescence: electron thermalization in xenon gas and xenon-nitrogen gas mixtures excited by 252Cffission fragments,Phys. Rev. A,25 (1982) 561–564.

    Article  Google Scholar 

  186. Takahashi T., Ruan(gen) J., Kubota S. andShiraishi F.,Time delay of recombination luminescence: electron thermalization in xenon gas and xenon-nitrogen gas mixtures excited by 252Cffission fragments,Phys. Rev. A,25 (1982) 600–603.

    Article  ADS  Google Scholar 

  187. Takahashi T., Ruan(gen) J., Kubota S. andShiraishi F.,Electron thermalization in argon-nitrogen gas mixture excited by 252Cffission fragments,Phys. Rev. A,25 (1982) 2820–2823.

    Article  ADS  Google Scholar 

  188. Takahashi T., Ruan(gen) J., Kubota S. andShiraishi F.,Time delay of recombination luminescence in xenon gas excited by 252Cffission fragments,Nucl. Instrum. Methods,196 (1982) 83–85.

    Article  ADS  Google Scholar 

  189. Takahashi T., Ruan(gen) J., Kubota S. andShiraishi F.,Time delay recombination in krypton gas excited by 252Cffission fragments: relation between electron energy relaxation and momentum-transfer cross section,Phys. Rev. A,32 (1985) 1211–1214.

    Article  ADS  Google Scholar 

  190. Takayanagi K. andItikawa Y.,Elementary processes involving electrons in the ionosphere,Space Sci Rev.,11 (1970) 380–450 e riferimenti citati.

    Article  ADS  Google Scholar 

  191. Tembe B. L. andMozumder A.,Electron thermalization in gases, V.Diatomic molecules H2, N2,and CO2,J. Chem. Phys.,78 (1983) 2030–2038.

    Article  ADS  Google Scholar 

  192. Tembe B. L. andMozumder A.,Electron thermalization in gas mixtures,Phys. Rev. A,27 (1983) 3274–3278.

    Article  ADS  Google Scholar 

  193. Tembe B. L. andMozumder A.,Transient electron mobility in pulse-irradiated gaseous argon under a steady field,J. Chem. Phys.,81 (1984) 2492–2495.

    Article  ADS  Google Scholar 

  194. Tendler M. andArora A.,Relaxation of an electron beam in a partially ionised plasma,J. Phys. D,11 (1978) 1125–1132.

    Article  ADS  Google Scholar 

  195. Tip A.,Time-evolution properties of a linear Boltzmann collision operator,J. Phys. A,15 (1982) 1159–1174.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  196. Vassell M. O.,Calculation of high-field distribution junctions in semiconductors,J. Math. Phys.,2 (1970) 408–412.

    Article  ADS  Google Scholar 

  197. Viehland L. A., Ranganathan S. andShizgal B.,Transient microwave conductivity of electrons in helium and argon,J. Chem. Phys.,88 (1988) 362–370.

    Article  ADS  Google Scholar 

  198. Warman J. M. andSauer M. C. jr.,Determination of electron thermalization times in irradiated gases, J. Chem. Phys.,52 (1970) 6428–6429.

    Article  ADS  Google Scholar 

  199. Warman J. M. andde Haas M. P.,The delayed absorption of microwaves due to electron thermalization in nanosecond puse irradiated N2, Heand Arat atmospheric pressure,J. Chem. Phys.,63 (1975) 2094–2100.

    Article  ADS  Google Scholar 

  200. Warman J. M. andSauer M. C. jr.,An investigation of electron thermalization in irradiated gases using CCI2 asan electron energy probe, J. Chem. Phys.,62 (1975) 1971–1981.

    Article  ADS  Google Scholar 

  201. Warman J. M., Sowada U. andde Haas M. P.,Transient negative mobility of hot electrons in gaseous xenon,Phys. Rev. A,31 (1985) 1974–1976. In questo riferimento viene impropriamente attribuito a McMahon e Shizgal (rif.McMahon et al. (1985)) il fenomeno delia possibile temporanea mobilità negativa di elettroni in Xe, predetto da Braglia e Ferrari fin dal 1971 (cfr. rif.Braglia et al (1971a)).

    Article  ADS  Google Scholar 

  202. Wilhelm J. andWinkler R.,Progress in the kinetic description of non-stationary behaviour of the electron ensemble in non-isothermal plasmas, XIV ICPIG,Grenoble 1979, and references therein. Reported inJ. Phys. (Paris),40 (1979) C7-251-C7-267.

  203. Williams M. M. R.,Mathematical Methods in Particle Transport Theory (London Butterworths, London) 1971.

    Google Scholar 

  204. Winkler R. andWilhelm J.,Solution of the non-stationary electron Boltzmann equation for a weakly ionized collision dominated plasma,Computer Phys. Comm.,20 (1980) 113–118.

    Article  ADS  Google Scholar 

  205. Winkler R., Braglia G. L., Hess A. andWilhelm J.,Fundamentals of a technique for determining electron distribution functions by multi-term even-order expansion in Legendre polynomials, I.Theory,Beitr. Plasmaphys.,24 (1984) 657–674.

    Article  ADS  Google Scholar 

  206. Winkler R., Wilhelm J. andBraglia G. L.,A new procedure for determining the diffusion coefficients of electron swarms according to the modern transport theory,Nuovo Cimento D,7 (1986) 641–680.

    Article  ADS  Google Scholar 

  207. Winkler R., Dilonardo M., Capitelli M. andWilhelm J.,Time-dependent solution of Boltzmann equation in RFplasmas. A comparison with the effective field approximation,Plasma Chem Plasma Process,7 (1987) 125–137.

    Article  Google Scholar 

  208. Winkler R., Braglia G. L. andWilhelm J.,Modification of the electron velocity distribution function in weakly ionized plasmas by non-isotropic elastic-scattering processes,Nuovo Cimento D,10 (1988) 1030–1060.

    ADS  Google Scholar 

  209. Winkler R., Braglia G. L. andWilhelm J.,Impact of non-isotropic elastic and inelastic scattering on the electron velocity distribution in weakly ionized plasmas,Nuovo Cimento D,10 (1988) 1209–1234.

    Article  ADS  Google Scholar 

  210. Winkler R., Braglia G. L. andWilhelm J.,Identification of main processes controlling the temporal relaxation of energetic electrons, XIX ICPIG (Oxford, 1989), Contributed papers, p. 174–175.

  211. Winkler R., Wilhelm J., Braglia G. L. andDiligenti M.,Multiterm calculations of electron energy distributions and transport coefficients in Arand Hg, II.Gas temperature effect,Nuovo Cimento D,12 (1990) 975–993.

    Article  ADS  Google Scholar 

  212. Winkler R. andWuttke M. W.,A detailed study of electron kinetics involved in modelling discharge pumped excvmer laser plasmas,Appl. Phys. B,54 (1992) 1–17.

    Article  ADS  Google Scholar 

  213. Winkler R., Loffhagen D. andBraglia G. L.,Non-stationary treatment of distribution anisotropy in the temporal relaxation of energetic electrons, XLVIIAnnual Gaseous Electronic Conference, Gaithersburg, 1994, Contributed papers, p. 1457.

  214. Winkler R., Braglia G. L. andWilhelm J.,Non-stationary treatment of distribution anisotropy in the temporal relaxation of an energetic electron group, Contr. Plasma Phys. (1995) in stampa.

  215. Wright B. L.,Microwave measurements of a time-dependent electron velocity distribution function,Quart. Prog. Rep.,80 (1966) 99–103.

    Google Scholar 

  216. Wright B. L.,Comparison of a measured time-dependent electron velocity distributions with a theoretical model,Quart. Prog. Rep.,83 (1966) 59–64.

    Google Scholar 

  217. Wright B. L.,Calculations of the time-dependent electron velocity distribution function in an argon afterglow plasma,Quart. Prog. Rep.,86 (1967) 134–138.

    Google Scholar 

  218. Young H. W. andMyers G. H.,Electron thermalization in a recombining plasma,Phys. Rev. A,11 (1975) 2134–2137.

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Fisica deU’Università, Viole delie Scienze, 43100, Parma, Italia

    G. L. Braglia

Authors
  1. G. L. Braglia
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Braglia, G.L. Teoria del trasporto elettronico in gas: processi di rilassamento. Riv. Nuovo Cim. 18, 1–162 (1995). https://doi.org/10.1007/BF02743023

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02743023

Search

Navigation