DC Super Layer 1:Layer 1 - Revision history

Vanwdani at 20:14, 15 May 2018

2018-05-15T20:14:00Z

Vanwdani: /* DC Super Layer 1:Layer 1 */

2017-05-26T18:54:08Z

DC Super Layer 1:Layer 1

Vanwdani: /* DC Super Layer 1:Layer 1 */

2017-05-26T18:29:38Z

DC Super Layer 1:Layer 1

Vanwdani: /* DC Super Layer 1:Layer 1 */

2017-05-26T18:28:56Z

DC Super Layer 1:Layer 1

Vanwdani: /* DC Super Layer 1:Layer 1 */

2017-05-26T18:28:09Z

DC Super Layer 1:Layer 1

Vanwdani: /* DC Super Layer 1:Layer 1 */

2017-05-26T18:21:38Z

DC Super Layer 1:Layer 1

Vanwdani: /* DC Super Layer 1:Layer 1 */

2017-05-26T16:47:31Z

DC Super Layer 1:Layer 1

Vanwdani at 16:41, 26 May 2017

2017-05-26T16:41:37Z

Vanwdani: /* DC Super Layer 1:Layer 1 */

2017-05-26T16:40:28Z

DC Super Layer 1:Layer 1

Vanwdani: /* DC Super Layer 1:Layer 1 */

2017-05-25T18:10:37Z

DC Super Layer 1:Layer 1

@@ Line 1: / Line 1: @@
-<center><math>\textbf{\underline{Navigation}}</math>
+<center><math>\underline{\textbf{Navigation}}</math>
 [[CED_Verification_of_DC_Angle_Theta_and_Wire_Correspondance|<math>\vartriangleleft </math>]]
@@ Line 255: / Line 255: @@
-<center><math>\textbf{\underline{Navigation}}</math>
+<center><math>\underline{\textbf{Navigation}}</math>
 [[CED_Verification_of_DC_Angle_Theta_and_Wire_Correspondance|<math>\vartriangleleft </math>]]

@@ Line 203: / Line 203: @@
-<center><math>\alpha=\arcsin{\frac{A \sin{\beta}}{B}}</math></center>
+<center><math>\Rightarrow \alpha=\arcsin{\frac{A \sin{\beta}}{B}}</math></center>
@@ Line 218: / Line 220: @@
 <center><math>\theta'\approx \Delta \theta=0.324556 -0.0000258\ n</math></center>
-does not give the same spacing between low and high values of n as seen in the calculated data.  The coefficient near the first order will have to smaller than .31 to find a correlation that would agree.
+does not give the same spacing between low and high values of n as seen in the calculated data.  The coefficient near the zeroth order for the derivative will have to be smaller than .31 to find a correlation that would agree with calculated values.
 Testing for a polynomial of degree 3 fit:
@@ Line 245: / Line 247: @@
-This is near the midpoint of the plane as seen in the geometry file.
+This is near the point of the plane where <math>\theta=25^{\circ}</math> as seen in the figure above.

← Older revision		Revision as of 18:29, 26 May 2017
Line 203:		Line 203:


−	<center><math>\alpha=\arcsin{\frac{A \sin{\beta}}}{B}</math></center>	+	<center><math>\alpha=\arcsin{\frac{A \sin{\beta}}{B}}</math></center>

← Older revision		Revision as of 18:28, 26 May 2017
Line 203:		Line 203:


−	<center><math>\alpha=\arcsin{\frac{A \sin{\beta}}{B}</math></center>	+	<center><math>\alpha=\arcsin{\frac{A \sin{\beta}}}{B}</math></center>

@@ Line 62: / Line 62: @@
-<center><math>\tan{\theta}=\frac{x-\Delta x+n\Delta x}{z-\Delta z+n\Delta z}\Rightarrow \theta=\arctan{\frac{x+n\Delta x}{z+n\Delta z}}</math></center>
+<center><math>\tan{\theta_n}=\frac{x-\Delta x+n\Delta x}{z-\Delta z+n\Delta z}\Rightarrow \theta_n=\arctan{\frac{x+n\Delta x}{z+n\Delta z}}</math></center>
 where
@@ Line 72: / Line 72: @@
-<center><math>\theta=\arctan{\frac{20.9972+n1.212}{243.1431-n0.5652}}</math></center>
+<center><math>\theta_n=\arctan{\frac{20.9972+n1.212}{243.1431-n0.5652}}</math></center>
-<center><math>\tan{\theta}=\frac{20.9972+n1.212}{243.1431-n0.5652}\Rightarrow \tan{ \theta}=-2.14437 + \frac{959.637}{430.189 - n}\Rightarrow 430.189 - n = \frac{959.637}{\tan{ \theta}+2.14437}</math></center>
+<center><math>\tan{\theta_n}=\frac{20.9972+n1.212}{243.1431-n0.5652}\Rightarrow \tan{ \theta_n}=-2.14437 + \frac{959.637}{430.189 - n}\Rightarrow 430.189 - n = \frac{959.637}{\tan{ \theta_n}+2.14437}</math></center>
-<center><math>\Rightarrow n = \frac{-959.637}{\tan{ \theta}+2.14437}+430.189</math></center>
+<center><math>\Rightarrow n = \frac{-959.637}{\tan{ \theta_n}+2.14437}+430.189</math></center>
 Using Mathematica, a series expansion about n=0 can be found:
@@ Line 197: / Line 197: @@
 [[File:Bin_angle_size.png|thumb|center|500px|alt=Geometry of Wire Bins Angular Size in DC|'''Figure 5.1.1:''' For a tilted plane, that is offset from the origin, the change in angle between uniformly spaced points depends on the tilt with respect to the beam line.  The uniform distance between points, A, can be used to show the angle, <math>\alpha</math> each wire bin covers can be found using the law of sines.  The interior angle <math>\beta</math>]]

← Older revision		Revision as of 18:21, 26 May 2017
Line 194:		Line 194:


−	~~<center>[[File:Bin_angle_size.png]]</center>~~	+

	[[File:Bin_angle_size.png\|thumb\|center\|500px\|alt=Geometry of Wire Bins Angular Size in DC\|'''Figure 5.1.1:''' For a tilted plane, that is offset from the origin, the change in angle between uniformly spaced points depends on the tilt with respect to the beam line. The uniform distance between points, A, can be used to show the angle, <math>\alpha</math> each wire bin covers can be found using the law of sines. The interior angle <math>\beta</math>]]		[[File:Bin_angle_size.png\|thumb\|center\|500px\|alt=Geometry of Wire Bins Angular Size in DC\|'''Figure 5.1.1:''' For a tilted plane, that is offset from the origin, the change in angle between uniformly spaced points depends on the tilt with respect to the beam line. The uniform distance between points, A, can be used to show the angle, <math>\alpha</math> each wire bin covers can be found using the law of sines. The interior angle <math>\beta</math>]]

← Older revision		Revision as of 16:47, 26 May 2017
Line 196:		Line 196:
	<center>[[File:Bin_angle_size.png]]</center>		<center>[[File:Bin_angle_size.png]]</center>

−		+	[[File:Bin_angle_size.png\|thumb\|center\|500px\|alt=Geometry of Wire Bins Angular Size in DC\|'''Figure 5.1.1:''' For a tilted plane, that is offset from the origin, the change in angle between uniformly spaced points depends on the tilt with respect to the beam line. The uniform distance between points, A, can be used to show the angle, <math>\alpha</math> each wire bin covers can be found using the law of sines. The interior angle <math>\beta</math>]]

@@ Line 2: / Line 2: @@
 [[CED_Verification_of_DC_Angle_Theta_and_Wire_Correspondance|<math>\vartriangleleft </math>]]
-[[CED_Verification_of_DC_Angle_Theta_and_Wire_Correspondance|<math>\triangle </math>]]
+[[VanWasshenova_Thesis#Determining_wire-theta_correspondence|<math>\triangle </math>]]
 [[DC_Binning_Based_On_Wire_Numbers|<math>\vartriangleright </math>]]

@@ Line 166: / Line 166: @@
-<center><math>\theta_{n=1}=\arctan{\frac{20.9972+(1)1.212}{243.1431-(1)0.5652}}</math></center>
+<center><math>\theta_{n=1}=\arctan{\frac{20.9972+(1)1.212}{243.1431-(1)0.5652}}=5.23\ \ \ \ \ \ \theta_{n=112}=\arctan{\frac{20.9972+(112)1.212}{243.1431-(112)0.5652}}=41.07</math></center>
 <center><math>\Delta degrees=41.07^{\circ}-5.23^{\circ}=35.84^{\circ}</math></center>
@@ Line 188: / Line 191: @@
-These differing values show that the bin width is not uniform in length, therefore a first order, linear fit, will not suffice.
+These differing values show that the bin width is not uniform in length, therefore a first order, linear fit, will not suffice.  The change in bin size, with respect to the angle theta covered, is due to the tilt of the wire plane.

@@ Line 181: / Line 181: @@
 Checking this, we can find the difference between wires 1 and 2,
-<center><math>\frac{\Delta degree}{\Delta wire\ number}=\frac{5.53^{\circ}-5.23^{\circ} }{wire\ number}=\frac{.3^{\circ}}{wire\ number} </math></center>
+<center><math>\frac{\Delta degree}{\Delta wire\ number}=\frac{5.5277^{\circ}-5.2311^{\circ} }{wire\ number}=\frac{.2965^{\circ}}{wire\ number} </math></center>
 Similarly, finding the difference between wires 111 and 112,
-<center><math>\frac{\Delta degree}{\Delta wire\ number}=\frac{41.07^{\circ}-40.76^{\circ}}{wire\ number}=\frac{.31^{\circ}}{wire\ number}</math></center>
+<center><math>\frac{\Delta degree}{\Delta wire\ number}=\frac{41.0740^{\circ}-40.7649^{\circ}}{wire\ number}=\frac{.0.3091^{\circ}}{wire\ number}</math></center>