GEM pre-amplification - Revision history

Abdehait: /* Townsend's First Coefficient */

2013-09-06T16:23:43Z

Townsend's First Coefficient

2013-09-05T13:34:05Z

Townsend's First Coefficient

2013-09-04T21:43:25Z

Townsend's First Coefficient

2013-09-04T21:42:27Z

Townsend's First Coefficient

2013-09-04T17:36:07Z

Townsend's First Coefficient

2013-09-04T17:34:48Z

Townsend's First Coefficient

2013-09-04T17:25:36Z

Townsend's First Coefficient

2013-09-04T17:16:28Z

Townsend's First Coefficient

2013-09-04T17:13:32Z

Townsend's First Coefficient

2013-09-04T17:12:52Z

Townsend's First Coefficient

← Older revision		Revision as of 16:23, 6 September 2013
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−	One of the ways to mathematically evaluate <math>\alpha/p</math> as a function of E/p is by the kinetic theory. The kinetic thory describes the gas' atoms and molecules energy and their collision rates depending on the mean free path of ionization. it defines the average mean free path by:	+	One of the ways to mathematically evaluate <math>\alpha/p</math> as a function of E/p is by the kinetic theory. The kinetic thory describes the gas atoms and molecules' energy and their collision rates depending on the mean free path of ionization. it defines the average mean free path by:

	<math> \bar{\lambda} = \frac{kT}{p \sigma_i} </math>		<math> \bar{\lambda} = \frac{kT}{p \sigma_i} </math>

@@ Line 21: / Line 21: @@
 [[Image:alpha_p_E_p_rations.png |thumb| Fig. shows alpha p ratio coincides with E p ratio <ref name="loeb"/>]]
-The relationship between <math>\alpha</math>/p and E/p is shown below, the equation can not predict all the values of <math>\alpha</math>/p accurately for different values  of E/p, i.e having a single analytical function to fit the experimental results for a gas does not exist, because <math>\alpha</math>/p is dependent on the number of electrons produced, the number changes as the average energy distribution of the ionizing electrons changes <ref name="loeb"/>.
+The relationship between <math>\alpha</math>/p and E/p is shown below, the equation can not predict all the values of <math>\alpha</math>/p accurately for different values  of E/p, i.e having a single analytical function to fit the experimental results for a gas does not exist, because <math>\alpha</math>/p is dependent on the number of electrons produced, the electrons number changes with changing the average energy distribution of the ionizing electrons <ref name="loeb"/>.
 <math> \frac {\alpha}{P}= Ae^{(\frac{-BP}{E})} </math>

@@ Line 32: / Line 32: @@
 where <math> \sigma_i </math> is the ionization cross section.
-<math> \alpha = -\frac{f'(x)}{dx} = 1/\bar{\lambda} e^{\lambda_i/\bar{\lambda}} \,\,\, f'(x) = e^{-x/\bar{lambda}} </math>
+<math> \alpha = -\frac{f'(x)}{dx} = 1/\bar{\lambda} e^{\lambda_i/\bar{\lambda}} \,\,\, f'(x) = e^{-x/\bar{\lambda}} </math>
 where x is the distance traveled by the electron. Substituting the value of <math> \lambda</math>

@@ Line 32: / Line 32: @@
 where <math> \sigma_i </math> is the ionization cross section.
-<math> \alpha = -\frac{f'(x)}{dx} = 1/bar{\lambda} e^{\lambda_i/\bar{\lambda}} \,\,\, f'(x) = e^{-x/\bar{lambda}} </math>
+<math> \alpha = -\frac{f'(x)}{dx} = 1/\bar{\lambda} e^{\lambda_i/\bar{\lambda}} \,\,\, f'(x) = e^{-x/\bar{lambda}} </math>
 where x is the distance traveled by the electron. Substituting the value of <math> \lambda</math>

@@ Line 44: / Line 44: @@
 <math> A = \frac{\sigma_i}{kT} \,\,\,\, and \,\,\, B = \frac {\sigma_i Vi}{kT} </math>
-The values for A and B do not always agree with the exprimetal values<Kuffel/>. Since it is assumed that if the electron energy is greaterthan <math>eV_i </math>, it will lead to ionization, however, the ionization probability does not always increase with increasing the the electron energy. Also the mean free path is defined as independent on the the electron energy, such a definition is not always true.
+The values for A and B do not always agree with the exprimetal values<Kuffel/>. Since it is assumed that if the electron energy is greaterthan <math>eV_i </math>, it will lead to ionization, however, the ionization probability does not always increase with increasing the the electron energy. Also the mean free path is defined as independent on the electron energy which is not always true.
 === Gas Quenching===

← Older revision		Revision as of 17:25, 4 September 2013
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	<math> A = \frac{\sigma_i}{kT} \,\,\,\, and \,\,\, B = \frac {\sigma_i Vi}{kT} </math>		<math> A = \frac{\sigma_i}{kT} \,\,\,\, and \,\,\, B = \frac {\sigma_i Vi}{kT} </math>
		+
		+	The values for A and B do not always agree with the exprimetal values<kuffel/>. since it is assumed that

	=== Gas Quenching===		=== Gas Quenching===

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 <math> \frac {\alpha}{P}= Ae^{(\frac{-BP}{E})} </math>
-Mathematically,  evaluating <math>\alpha/p</math> as a function of E/p using the kinetic theory disagrees with experimental values. The kinetic thory describes the gas' atoms and molecules energy and their collision rates depending on the mean free path of ionization. it defines the average mean free path by:
 <math>  \bar{\lambda} = \frac{kT}{p \sigma_i} </math>

← Older revision		Revision as of 17:12, 4 September 2013
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−	<math> frac{\alpha}{p} = \frac{\sigma_i}{kT} e^{-\sigma_i/kT (V_i/(E/p))} = A e^{-B/(E/T)} </math>	+	<math> \frac{\alpha}{p} = \frac{\sigma_i}{kT} e^{-\sigma_i/kT (V_i/(E/p))} = A e^{-B/(E/T)} </math>
		+
		+
		+	where ;
		+
		+	<math> A = \frac{\sigma_i}{kT} \,\,\,\, and \,\,\, B = \frac {-\sigma_i Vi}{kT} </math>

	=== Gas Quenching===		=== Gas Quenching===