Magnet - Revision history

Oborn at 18:05, 22 May 2009

2009-05-22T18:05:33Z

Oborn at 18:04, 22 May 2009

2009-05-22T18:04:59Z

Oborn at 18:02, 22 May 2009

2009-05-22T18:02:32Z

Oborn at 18:01, 22 May 2009

2009-05-22T18:01:20Z

Oborn at 18:00, 22 May 2009

2009-05-22T18:00:56Z

Oborn at 16:35, 22 May 2009

2009-05-22T16:35:07Z

Oborn at 16:26, 22 May 2009

2009-05-22T16:26:48Z

Oborn at 16:22, 22 May 2009

2009-05-22T16:22:59Z

Oborn: New page: [http://wiki.iac.isu.edu/index.php/Pair_Spectrometer_Calculations Go Back]

2009-05-22T16:20:51Z

New page: [http://wiki.iac.isu.edu/index.php/Pair_Spectrometer_Calculations Go Back]

New page

[http://wiki.iac.isu.edu/index.php/Pair_Spectrometer_Calculations Go Back]

@@ Line 8: / Line 8: @@
 Current: <math>138 A</math>
-Resistance:  <math>0.116 \Ohm</math>
+Resistance:  <math>0.116 Ohm</math>
 Voltage: <math>V=IR=16.008 V</math>

@@ Line 8: / Line 8: @@
 Current: <math>138 A</math>
-Resistance:  <math>0.116 {\ohm}</math>
+Resistance:  <math>0.116 \Ohm</math>
 Voltage: <math>V=IR=16.008 V</math>

@@ Line 8: / Line 8: @@
 Current: <math>138 A</math>
-Resistance:  <math>0.116 ohm</math>
+Resistance:  <math>0.116 {\ohm}</math>
 Voltage: <math>V=IR=16.008 V</math>

@@ Line 4: / Line 4: @@
 TESLA ENGINEERING:  7 Degree Bend Angle Dipole
-<math>B_(max)=0.35 T</math>
+<math>B_{max}=0.35 T</math>
 Current: <math>138 A</math>

@@ Line 4: / Line 4: @@
 TESLA ENGINEERING:  7 Degree Bend Angle Dipole
-<math>B=0.35 T</math>
+<math>B_(max)=0.35 T</math>
 Current: <math>138 A</math>

← Older revision		Revision as of 16:35, 22 May 2009
Line 123:		Line 123:


−	[http://wiki.iac.isu.edu/index.php/~~Pair_Spectrometer_Calculations~~ Go Back]	+	[http://wiki.iac.isu.edu/index.php/Pair_Spectrometer_Info Go Back]

← Older revision		Revision as of 16:26, 22 May 2009
Line 17:		Line 17:

	== CALCULATIONS ==		== CALCULATIONS ==
		+
		+	'''Radius of Curvature'''
		+
		+
		+	Below are my calculations done for determining the radius of curvature of an electron/positron in the magnetic field for the pair spectrometer.
		+
		+	The Lorentz force is the centripetal force acting upon the electron/positron in the magnetic field which gives the following equation.
		+
		+	<math>\frac{(mv^2)}{r} = q v * B </math>
		+
		+	This equation can be rearranged to solve for r (and given that mv = momentum) to give the following equation
		+
		+	<math>r = \frac{\rho}{q*B}</math>
		+
		+	For this sample equation 1 MeV will be used to determine the radius of curvature per MeV of the incident beam.
		+
		+	Energy = 1 MeV = <math> 1 * 10^6 \frac{J}{C} * 1.6022 * 10^{-19}C = 110^6\frac{kg m^2}{s^2 * C} * 1.6022 * 10^{-19}C </math>
		+
		+	Magnetic Field (B) = 0.35 Tesla = <math>0.35\frac{kg}{C*s}</math>
		+
		+	Charge of an electron (q) = <math>1.6022 * 10^{19} Coulombs</math>
		+
		+	To get the momentum of the positron/electron the energy of the particle is divided by the speed of the particle (ie <math> 2.99 * 10^8 \frac
		+	{m}{s})</math>
		+
		+	Substituting the numbers above into the radius equation gives the following
		+
		+	<math> \frac{(110^6 \frac{kgm^2}{s^2C}) (1.6022 * 10^{-19}C)}{(2.9910^8\frac{m}{s})(0.35\frac{kg}{Cs})(1.6022 * 10^{-19}C)} =
		+	0.009556 meters = 0.9556 cm</math>
		+
		+	So basically the radius of curvature for the electrons/positrons is ~0.9556cm per MeV
		+
		+	So for a 7 MeV electron/positron pair the radius of curvature for either particle in a 0.35 T field would be 6.69cm
		+
		+
		+
		+
	'''Calculating the Magnetic Field Needed:'''		'''Calculating the Magnetic Field Needed:'''

← Older revision		Revision as of 16:22, 22 May 2009
Line 1:		Line 1:
		+	== Specs: ==
		+
		+
		+	TESLA ENGINEERING: 7 Degree Bend Angle Dipole
		+
		+	<math>B=0.35 T</math>
		+
		+	Current: <math>138 A</math>
		+
		+	Resistance: <math>0.116 ohm</math>
		+
		+	Voltage: <math>V=IR=16.008 V</math>
		+
		+	Water Flow: <math>1.2 L/minute</math>
		+
		+
		+
		+	== CALCULATIONS ==
		+	'''Calculating the Magnetic Field Needed:'''
		+
		+	Lorentz Force equation: F=q(v×B)
		+
		+	Electron moves through the magnetic field B accelerated by force F proportional to the component of velocity perpendicular to the field B and velocity v. Moves with constant kinetic energy and speed due to the fact that the magnetic field never does work on the particle since the always moves perpendicular to the force.
		+
		+	Magnetic force: <math>F=evB</math>
		+
		+	The radius of the arc can be through: <math>(mv^2)/R=ev*B</math>
		+
		+	giving: <math>R=mv/eB</math>
		+
		+	The length of the circular arc is S and the deflection angle is found as: sin(θ)=S/R
		+
		+	For small θ, and large R, the arc length S will be approx L, giving: sin(θ)=L/R=LeB/m*v
		+
		+	Giving θ=sin^(-1)(cBL/p)
		+
		+	The displacement is found as: d=R-Rcos(θ)=mv/eB(1-cos(θ))
		+
		+	Table: Data for B=0.0078 T.
		+	{\| border="1" cellpadding="2"
		+	!width="70"\|Momentum
		+	!width="70"\|Radius of Curvature
		+	!width="70"\|Bend Angle
		+	!width="70"\|Bend Angle
		+	!width="70"\|Displacement @ end of magnet
		+
		+	\|-
		+
		+	\|P (MeV)\|\|R (m)\|\|θ (radians)\|\|θ (degrees)\|\|d (cm)
		+	\|-
		+	\|1\|\|0.43\|\|0.70\|\|40.02\|\|10.01
		+	\|-
		+	\|2\|\|0.86\|\|0.33\|\|18.76\|\|4.54
		+	\|-
		+	\|3\|\|1.28\|\|0.22\|\|12.38\|\|2.98
		+	\|-
		+	\|4\|\|1.71\|\|0.16\|\|9.25\|\|2.22
		+	\|-
		+	\|5\|\|2.14\|\|0.13\|\|7.39\|\|1.78
		+	\|-
		+	\|6\|\|2.57\|\|0.11\|\|6.15\|\|1.48
		+	\|-
		+	\|7\|\|2.99\|\|0.09\|\|5.27\|\|1.27
		+	\|-
		+	\|8\|\|3.42\|\|0.08\|\|4.61\|\|1.11
		+	\|-
		+	\|9\|\|3.85\|\|0.07\|\|4.10\|\|0.98
		+	\|-
		+	\|10\|\|4.28\|\|0.06\|\|3.69\|\|0.89
		+	\|-
		+	\|11\|\|4.70\|\|0.06\|\|3.35\|\|0.80
		+	\|-
		+	\|12\|\|5.13\|\|0.05\|\|3.07\|\|0.74
		+	\|-
		+	\|13\|\|5.56\|\|0.05\|\|2.84\|\|0.68
		+	\|-
		+	\|14\|\|5.99\|\|0.05\|\|2.63\|\|0.63
		+	\|-
		+	\|15\|\|6.41\|\|0.04\|\|2.46\|\|0.59
		+	\|-
		+	\|16\|\|6.84\|\|0.04\|\|2.30\|\|0.55
		+	\|}
		+
		+
		+
		+
		+
	[http://wiki.iac.isu.edu/index.php/Pair_Spectrometer_Calculations Go Back]		[http://wiki.iac.isu.edu/index.php/Pair_Spectrometer_Calculations Go Back]