Sadiq IPAC 2013 - Revision history

Setisadi: /* convert to latex */

2013-05-18T03:51:27Z

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Setisadi: /* convert to latex */

2013-05-17T04:19:54Z

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Setisadi: /* Title: Linac Based Positron Production */

2013-05-17T04:19:01Z

Title: Linac Based Positron Production

Setisadi at 19:45, 12 November 2012

2012-11-12T19:45:22Z

Setisadi: Created page with "Positron production using S-band High Repetition Rate Linac (HRRL) was performed at Idaho State University's Idaho Accelerator Center (IAC). Positrons were produced by impinging …"

2012-11-12T19:39:50Z

Created page with "Positron production using S-band High Repetition Rate Linac (HRRL) was performed at Idaho State University's Idaho Accelerator Center (IAC). Positrons were produced by impinging …"

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Positron production using S-band High Repetition Rate Linac (HRRL) was performed at Idaho State University's Idaho Accelerator Center (IAC). Positrons were produced by impinging electrons to a tungsten foil. Bremsstrahlung photons generated in the tungsten foil pair produces electron and positrons. In this paper, we describe the production, transportation and detection of positrons when electron beam energy is 15 MeV.

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 = convert to latex =
-The Cross section formula is given in Formula 3Cs, pg 928 of reference [http://www.physics.isu.edu/~tforest/Classes/NucSim/Day8/BremXsectFormula_Rev.Mod.Phys_vol31_pg920_1959.pdf H.W. Koch & J.W Motz, Rev. Mod. Phys., vol 31 (1959) pg 920] as
+where
-where
+:<math>k =</math> photon momentum/energy
-: <math>E_0</math> = initial total energy of the electron
+;Note: The above equations for the differential cross section are using "natural" units where <math>c  \equiv 1</math>

← Older revision		Revision as of 04:19, 17 May 2013
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	:<math>\alpha = \frac{1}{137}</math>		:<math>\alpha = \frac{1}{137}</math>
	: <math>\phi_1</math> and <math>\phi_2</math> = screening functions that depend on Z		: <math>\phi_1</math> and <math>\phi_2</math> = screening functions that depend on Z
−
−	~~if <math>Z \ge 5</math>~~
−
−	~~:<math>\phi_1(\gamma) = 20.863 - 2 \ln[1+(0.55 \gamma)^2] - 4[1-0.6e^{-0.98} - 0.4e^{-3 \gamma/2}]</math>~~
−	~~:<math>\phi_2(\gamma) = \phi_1(\gamma) - \frac{2}{3}(1+6.5 \gamma + 6 \gamma^2)</math>~~
−
−
−	~~For Z<5 see [http://www.physics.isu.edu/~tforest/Classes/NucSim/Day8/Tsai_ScreeningFunctions_Rev.Mod.Phys._vol46_pg815_1974.pdf Tsai, Rev.Mod. Phys., vol 46 (1974) pg 815]~~
−
−	~~:if <math>3 \ge Z < 5</math> use Equation 3.46 and 3.47~~
−
−	~~:if <math> Z < 2</math> use Equation 3.25 and 3.26~~

← Older revision		Revision as of 04:19, 17 May 2013
Line 4:		Line 4:

	Positron production using S-band High Repetition Rate Linac (HRRL) was performed at Idaho State University's Idaho Accelerator Center (IAC). Positrons were produced by impinging electrons to a tungsten foil. Bremsstrahlung photons generated in the tungsten foil pair produces electron and positrons. In this paper, we describe the production, transportation and detection of positrons when electron beam energy is 15 MeV.		Positron production using S-band High Repetition Rate Linac (HRRL) was performed at Idaho State University's Idaho Accelerator Center (IAC). Positrons were produced by impinging electrons to a tungsten foil. Bremsstrahlung photons generated in the tungsten foil pair produces electron and positrons. In this paper, we describe the production, transportation and detection of positrons when electron beam energy is 15 MeV.
		+
		+
		+	= convert to latex =
		+
		+
		+	The Cross section formula is given in Formula 3Cs, pg 928 of reference [http://www.physics.isu.edu/~tforest/Classes/NucSim/Day8/BremXsectFormula_Rev.Mod.Phys_vol31_pg920_1959.pdf H.W. Koch & J.W Motz, Rev. Mod. Phys., vol 31 (1959) pg 920] as
		+
		+	;Note: Bethe & Heitler first calculated this radiation in 1934 which is why you will sometimes hear Bremsstrahlung radiation refererd to as Bethe-Heitler.
		+
		+	:<math>d \sigma = 4 Z^2r_e^2 \alpha \frac{d \nu}{\nu} \left \{ \left (1 + \left( \frac{E}{E_0} \right )^2 \right ) \left [ \frac{\phi_1(\gamma)}{4} - \frac{1}{3} \ln Z -f(Z)\right ] - \frac{2E}{3E_0} \left [ \frac{\phi_2(\gamma)}{4} - \frac{1}{3} \ln Z -f(Z)\right ] \right \} </math>
		+
		+	where
		+
		+	: <math>E_0</math> = initial total energy of the electron
		+	:<math>E</math> = final total energy of the electron
		+	: <math>\nu = \frac{E_0-E}{h}</math> = energy of the emitted photon
		+	:<math>Z</math> = Atomic number = number of protons in target material
		+	: <math>\gamma = \frac{100 m_ec^2 h \nu}{E_0 E Z^{1/3}}</math> = charge screening parameter
		+	Coulomb correction to using the Born approximation (approximation assumes the incident particle is a plane wave interacting with a static E-field the correction accounts for changes iin the plane wave due to the presence of the field) Charge screening and the coulomb correction are different effects that have been shown to be additive/independent. [[File:Haug_2008.pdf]]
		+	:<math>f(Z) = (Z \alpha)^2 \sum_1^{\infty} \frac{1}{ n [ n^2 + (Z \alpha)^2]}</math>
		+	: <math>\sim (Z \alpha)^2 \left \{ \frac{1}{1+(Z \alpha)^2} +0.20206 - 0.0369(Z \alpha)^2 + 0.0083 (Z \alpha)^4 - 0.002 (Z \alpha)^6\right \}</math>
		+	:<math>\alpha = \frac{1}{137}</math>
		+	: <math>\phi_1</math> and <math>\phi_2</math> = screening functions that depend on Z
		+
		+	if <math>Z \ge 5</math>
		+
		+	:<math>\phi_1(\gamma) = 20.863 - 2 \ln[1+(0.55 \gamma)^2] - 4[1-0.6e^{-0.98} - 0.4e^{-3 \gamma/2}]</math>
		+	:<math>\phi_2(\gamma) = \phi_1(\gamma) - \frac{2}{3}(1+6.5 \gamma + 6 \gamma^2)</math>
		+
		+
		+	For Z<5 see [http://www.physics.isu.edu/~tforest/Classes/NucSim/Day8/Tsai_ScreeningFunctions_Rev.Mod.Phys._vol46_pg815_1974.pdf Tsai, Rev.Mod. Phys., vol 46 (1974) pg 815]
		+
		+	:if <math>3 \ge Z < 5</math> use Equation 3.46 and 3.47
		+
		+	:if <math> Z < 2</math> use Equation 3.25 and 3.26

← Older revision		Revision as of 19:45, 12 November 2012
Line 1:		Line 1:
		+	=Title: Linac Based Positron Production=
		+
		+
		+
	Positron production using S-band High Repetition Rate Linac (HRRL) was performed at Idaho State University's Idaho Accelerator Center (IAC). Positrons were produced by impinging electrons to a tungsten foil. Bremsstrahlung photons generated in the tungsten foil pair produces electron and positrons. In this paper, we describe the production, transportation and detection of positrons when electron beam energy is 15 MeV.		Positron production using S-band High Repetition Rate Linac (HRRL) was performed at Idaho State University's Idaho Accelerator Center (IAC). Positrons were produced by impinging electrons to a tungsten foil. Bremsstrahlung photons generated in the tungsten foil pair produces electron and positrons. In this paper, we describe the production, transportation and detection of positrons when electron beam energy is 15 MeV.