Simulating Particle Trajectories - Revision history

Oborn at 17:56, 18 June 2009

2009-06-18T17:56:22Z

Oborn at 22:37, 17 June 2009

2009-06-17T22:37:44Z

Oborn at 22:09, 17 June 2009

2009-06-17T22:09:58Z

Oborn at 22:08, 17 June 2009

2009-06-17T22:08:58Z

Oborn at 22:07, 17 June 2009

2009-06-17T22:07:16Z

Oborn at 22:06, 17 June 2009

2009-06-17T22:06:47Z

Oborn at 20:12, 11 June 2009

2009-06-11T20:12:44Z

Oborn at 22:53, 10 June 2009

2009-06-10T22:53:51Z

Oborn at 22:53, 10 June 2009

2009-06-10T22:53:29Z

Oborn at 22:52, 10 June 2009

2009-06-10T22:52:28Z

@@ Line 3: / Line 3: @@
 '''Description of Problem'''
-The general problem of modeling relativistic particle trajectories in electromagnetic fields boils down to solving the following system of six differential equations:
+Essentially what we need to do is determine the trajectory of charged particles in an electromagnetic field. In simple cases, such as when the fields are uniform, the appropriate set of dynamical equations can be solved analytically. However, for the "silver" permanent magnet we plan on using for the pair spectrometer, the fields are anything but uniform. In such a case, the system must be solved numerically.
 '''Description of PAIRSPEC Code'''

@@ Line 13: / Line 13: @@
 In simple cases, such as when the fields are uniform, this set of equations can be solved analytically. However, for the "silver" permanent magnet we plan on using for the pair spectrometer, the fields are anything but uniform. In such a case, the system must be solved numerically.
-'''Description of Code'''
+'''Description of PAIRSPEC Code'''
 The code, [[New Particle Trajectory Code|found here]], solves the above system of equations using an embedded 8th order Runge-Kutta Prince-Dormand method with 9th order error estimates with adaptive stepsize control, as implemented in the GNU Scientific Library [http://www.gnu.org/software/gsl]. The files include the relevant source and a script which should build the executable on any unix system with GSL installed in the usual place. The program also requires the ncurses library (standard with just about any linux distribution), the PGPLOT graphics library [http://www.astro.caltech.edu/~tjp/pgplot/], and the RDYNLAB library [[RDYNLAB|found here]].

@@ Line 67: / Line 67: @@
 For the "interactive mode", the input file is identical to the input file for "detailed mode", with the exception of the -1 on the first line. The trajectories are plotted to the screen, and a control dialog appears in the terminal, as shown in the screenshot below. Upon exiting, the program writes a "detailed mode" input file for the last adjustment to "pairspec.in".
-[[Image:pairspec_screenshot.jpg|thumb]]
+[[Image:pairspec_screenshot.jpg|600px]]
 An older version of the code that did not include all of the features and had more limitations, and wrote different output flags can be found [[Particle Trajectory Code|here]].

@@ Line 67: / Line 67: @@
 For the "interactive mode", the input file is identical to the input file for "detailed mode", with the exception of the -1 on the first line. The trajectories are plotted to the screen, and a control dialog appears in the terminal, as shown in the screenshot below. Upon exiting, the program writes a "detailed mode" input file for the last adjustment to "pairspec.in".
-[[Image:pairspec_screenshot.jpg]]
+[[Image:pairspec_screenshot.jpg|thumb]]
 An older version of the code that did not include all of the features and had more limitations, and wrote different output flags can be found [[Particle Trajectory Code|here]].

@@ Line 15: / Line 15: @@
 '''Description of Code'''
-The code, [[New Particle Trajectory Code|found here]], solves the above system of equations using an embedded 8th order Runge-Kutta Prince-Dormand method with 9th order error estimates with adaptive stepsize control, as implemented in the GNU Scientific Library [http://www.gnu.org/software/gsl|(link)]. The files include the relevant source and a script which should build the executable on any unix system with GSL installed in the usual place. The program also requires the ncurses library (standard with just about any linux distribution), the PGPLOT graphics library [http://www.astro.caltech.edu/~tjp/pgplot/|(link)], and the RDYNLAB library [[RDYNLAB|found here]].
+The code, [[New Particle Trajectory Code|found here]], solves the above system of equations using an embedded 8th order Runge-Kutta Prince-Dormand method with 9th order error estimates with adaptive stepsize control, as implemented in the GNU Scientific Library [http://www.gnu.org/software/gsl]. The files include the relevant source and a script which should build the executable on any unix system with GSL installed in the usual place. The program also requires the ncurses library (standard with just about any linux distribution), the PGPLOT graphics library [http://www.astro.caltech.edu/~tjp/pgplot/], and the RDYNLAB library [[RDYNLAB|found here]].
 When executing the code, you must specify an input file on the command line. The input file is fairly simple. The first line of the input file is either a "0" or some integer greater than zero, and tells the program to run in "detailed output" or "scan" mode, respectively. In the latest version of the code, an interactive mode is also available by putting a -1 on this first line.

@@ Line 15: / Line 15: @@
 '''Description of Code'''
-The code, [[Particle Trajectory Code|found here]], solves the above system of equations using an embedded 8th order Runge-Kutta Prince-Dormand method with 9th order error estimates with adaptive stepsize control, as implemented in the GNU Scientific Library [http://www.gnu.org/software/gsl]. The files include the relevant source and a script which should build the executable on any unix system with GSL installed in the usual place.
+The code, [[New Particle Trajectory Code|found here]], solves the above system of equations using an embedded 8th order Runge-Kutta Prince-Dormand method with 9th order error estimates with adaptive stepsize control, as implemented in the GNU Scientific Library [http://www.gnu.org/software/gsl|(link)]. The files include the relevant source and a script which should build the executable on any unix system with GSL installed in the usual place. The program also requires the ncurses library (standard with just about any linux distribution), the PGPLOT graphics library [http://www.astro.caltech.edu/~tjp/pgplot/|(link)], and the RDYNLAB library [[RDYNLAB|found here]].
-When executing the code, you must specify an input file on the command line. The input file is fairly simple. The first line of the input file is either a "0" or some integer greater than zero, and tells the program to run in "detailed output" or "scan" mode, respectively. In "detailed output" mode, the next five lines specify the energy of the initial gamma ray, the energy of the electron (the energy of the positron is assumed to be the difference of these two numbers), the angle between the axis of the magnet and the photon beam, the "Y" position of the conversion site above the magnet yoke, and the "X" position of the conversion site relative to the left edge of the magnet. In "scan" mode, the integer on the first line tells the program how many cases to run. Only two additional lines are needed: the energy of the photon and the "X" position of the conversion site. Examples of such input files are provided [[Media:trajectory_input_0.txt|here (detailed mode)]] and [[Media:trajectory_input_1.txt|here (scan mode)]].
+When executing the code, you must specify an input file on the command line. The input file is fairly simple. The first line of the input file is either a "0" or some integer greater than zero, and tells the program to run in "detailed output" or "scan" mode, respectively. In the latest version of the code, an interactive mode is also available by putting a -1 on this first line.
 The program output also depends on the program mode. In the "detailed output" mode, everything is written to stdout, and can be directed to a file using the ">" director. The output begins with a header, each line of which begins with the "#" character. The header lists the physical properties of the particle, the conditions read from the input file, and the corresponding initial positions and momenta of the electron and positron. Following the header, the program writes four columns of data: the time (in seconds) and the x, y, and z coordinates (in meters).
@@ Line 27: / Line 29: @@
 |-
 |  0
-|  Electron hits the yoke
+|  Both particles have exit angles greater than 90 degrees (ideal)
 |-
 |  1
-|  Neither particle has an exit angle greater than 90 degrees
+|  Only the electron has an exit angle greater than 90 degrees
 |-
 |  2
-|  Only the electron has an exit angle greater than 90 degrees
+|  Only the positron has an exit angle greater than 90 degrees
 |-
 |  3
-|  Only the positron has an exit angle greater than 90 degrees
+|  Neither particle has an exit angle greater than 90 degrees, but both leave the magnet.
 |-
 |  4
-|  Both particles have exit angles greater than 90 degrees (ideal)
+|  The electron hits the yoke
 |-
 |  5
-|  The electron gets trapped in the magnetic field
+|  The positron hits the yoke
 |-
 |  6
-|  The positron gets trapped in the magnetic field
+|  Both particles hit the yoke
 |}
@@ Line 53: / Line 64: @@
 Progress output is written to stderr, and for each run that results in a flag greater than one an input file (for "detailed output" mode) is written.
@@ Line 74: / Line 91: @@
-'''Limitations of the Code'''
+'''Radiative Power Loss'''
-The code does not take into account any power radiated away as the charged particles accelerate. Such power loss is given by the Lienard formula,
+The code accounts for power radiated away as the charged particles accelerate. Such power loss is given by the Lienard formula,
 <math>
 \frac{dE}{dt}=-\frac{\mu_0q^2\gamma^6}{6\pi c}\left(\vec{a}\cdot\vec{a}-\left|\frac{\vec{v}\times\vec{a}}{c}\right|^2\right)</math>
-For energies and speeds typical of what we expect to see in the pair spectrometer, these power losses are negligible. Future iterations of the code may include such power losses, but their value to the current problem when compared to the difficulty of implementing such losses does not justify the task for the time being.
+For energies and speeds typical of what we expect to see in the pair spectrometer, these power losses are negligible. The code includes such power losses through the RDYNLAB library.

← Older revision		Revision as of 20:12, 11 June 2009
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	[[Image:magnet_parameter_scan_10.jpg\|Scan of parameter space for 10 MeV gamma rays]]		[[Image:magnet_parameter_scan_10.jpg\|Scan of parameter space for 10 MeV gamma rays]]

−	The points in red represent parameter sets where the electron leaves the magnetic field with an exit angle greater than 90 degrees. The green points represent a similar condition for the positron, and the blue points represent parameter sets where both particles leave with exit angles greater than 90 degrees (our "ideal" scenario). It can be seen that ~~the~~ ideal parameter space ~~is larger~~ for ~~the lower energy photons (not surprisingly)~~, ~~but there~~ is ~~still~~ a significant set of parameters at 5 MeV incident energy that meet the ideal criteria.	+	The points in red represent parameter sets where the electron leaves the magnetic field with an exit angle greater than 90 degrees. The green points represent a similar condition for the positron, and the blue points represent parameter sets where both particles leave with exit angles greater than 90 degrees (our "ideal" scenario). It can be seen that ideal parameter space exists for incident photon energies of 3, 4, and 5 MeV. There is a significant set of parameters at 5 MeV incident energy that meet the ideal criteria.

← Older revision		Revision as of 22:53, 10 June 2009
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	It is possible that the photons will pair produce in air at other locations on the beam, or that the electron produced will not carry 3.5 MeV of the total energy. [[Media:air_converted_pairs.pdf\|This document]] shows the trajectories for the particles in these other scenarios. The electron energy and the "X" position of the conversion site are shown at the top of each graph. The black circles represent possible locations for the detectors. It appears that only the parameters described above will cause a coincidence in both detectors.		It is possible that the photons will pair produce in air at other locations on the beam, or that the electron produced will not carry 3.5 MeV of the total energy. [[Media:air_converted_pairs.pdf\|This document]] shows the trajectories for the particles in these other scenarios. The electron energy and the "X" position of the conversion site are shown at the top of each graph. The black circles represent possible locations for the detectors. It appears that only the parameters described above will cause a coincidence in both detectors.
		+
		+
	[http://wiki.iac.isu.edu/index.php/Pair_Spectrometer_Info Go Back]		[http://wiki.iac.isu.edu/index.php/Pair_Spectrometer_Info Go Back]

← Older revision		Revision as of 22:52, 10 June 2009
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	It is possible that the photons will pair produce in air at other locations on the beam, or that the electron produced will not carry 3.5 MeV of the total energy. [[Media:air_converted_pairs.pdf\|This document]] shows the trajectories for the particles in these other scenarios. The electron energy and the "X" position of the conversion site are shown at the top of each graph. The black circles represent possible locations for the detectors. It appears that only the parameters described above will cause a coincidence in both detectors.		It is possible that the photons will pair produce in air at other locations on the beam, or that the electron produced will not carry 3.5 MeV of the total energy. [[Media:air_converted_pairs.pdf\|This document]] shows the trajectories for the particles in these other scenarios. The electron energy and the "X" position of the conversion site are shown at the top of each graph. The black circles represent possible locations for the detectors. It appears that only the parameters described above will cause a coincidence in both detectors.
		+
		+	[http://wikhttp://wiki.iac.isu.edu/index.php/Pair_Spectrometer_Info Go Back]