Statistics of electron avalanches and ultimate resolution of proportional counters

Abstract This paper deals with the fundamental limitations set on the ultimate energy resolving power of a proportional counter. An analysis of a few statistical models of electron avalanches in gases subjected to uniform electric fields is performed. A formula for gas amplification variance in non-uniform fields is derived. The relative variance of gas amplification in argon and methane filled cylindrical proportional counters for the case of K = 10 2 –10 5 and pr a = 1–4 torr·cm is calculated to be 0.6 to 0.8. The present work shows that avalanche size distributions in uniform fields are close to those computed by Legler, but that the distributions in the non-uniform fields of cylindrical counters are close to those of Polya-type.

[1]  J. Byrne,et al.  Statistics of electron avalanches in the proportional counter , 1969 .

[2]  G. Alkhazov.  Mean value and variance of gas amplification in proportional counters , 1969 .

[3]  W. Legler.  The influence of the relaxation of the electron energy distribution on the statistics of electron avalanches , 1967 .

[4]  U. Fano.  Ionization Yield of Radiations. II. The Fluctuations of the Number of Ions , 1947 .

[5]  H. Schlumbohm.  Zur Statistik der Elektronenlawinen im ebenen Feld. III , 1958 .

[6]  A. Kruithof,et al.  Determination of the Townsend ionization coefficient α for pure argon , 1936 .

[7]  E. F. Bennett,et al.  ELECTRON MULTIPLICATION PROCESS IN PROPORTIONAL COUNTERS , 1966 .

[8]  T. Mulvey,et al.  Proportional counters in x-ray spectro-chemical analysis , 1958 .

[9]  R. Wijsman.  Breakdown Probability of a Low Pressure Gas Discharge , 1949 .

[10]  B. Pontecorvo,et al.  High Multiplication Proportional Counters for Energy Measurements , 1949 .

[11]  T. Lewis,et al.  Townsend's first ionization coefficient for methane and nitrogen , 1966 .

[12]  K. Ledingham,et al.  Pulse height distributions from proportional counters , 1966 .

[13]  S. Curran,et al.  LXXXVI. Investigation of soft radiation by proportional counters—V. Use as a detector of ultra-violet quanta and analysis of the gas multiplication process , 1949 .

[14]  G. D. Alkhazov,et al.  Ionization fluctuations and resolution of ionization chambers and semiconductor detectors , 1967 .

[15]  B. A. Cooke,et al.  PROPORTIONAL COUNTER RESOLUTION. , 1968 .

[16]  Leendert Vriens.  Binary-Encounter Electron-Atom Collision Theory , 1966 .

[17]  T. Lewis,et al.  VARIATIONS IN THE TOWNSEND FIRST IONIZATION COEFFICIENT FOR GASES. , 1966 .

[18]  W. Legler.  Zur Statistik der Elektronenlawinen , 1955 .