Changes between Version 1 and Version 2 of PolarizationMaps

Timestamp:

05/01/18 15:46:59 (8 years ago)

Author:

Jonathan

Comment:

—

PolarizationMaps

@@ +1 @@
+Goal is to integrate various functions along lines of sight which is constrained to be in the y-z plane.  
+
+$\int f(B_\perp(s), B_x(s)) ds$
+
+$B_\perp(s) = B_y(s) \cos(\theta) + B_z(s) \sin(\theta)$
+
+
+Each pixel will be given by the integral of the function along the path
+
+$s = x_i, y_i+s \sin(\theta), z_i+s \cos(\theta)$
+
+where $\delta y = \cos(\theta) \delta x$ and $\delta z =\sin(\theta) \delta x$
+
+
+For 3D we just need to create the expressions in visit, create the expressions and the lineouts, and then integrate the resulting query
+
+
+For 2.5D, we need to transform the integral along $s$ into an integral in the $xy$ plane.
+
+
+
+
+
+
+Assume jet is oriented along $y$ and that we are integrating along the direction $(0, sin(\theta), cos(\theta))$
+
+where $\theta$ is the angle of inclination.
+
+We are interested in calculating the integral of $B_p^2$, $B_x^2$, and $B_xB_p$ where $B_p = cos(\theta)By + sin(\theta)Bz$
+
+If $\theta = 0$ this is just $\int B_y^2 dz$, $\int B_x^2 dz$, and $\int B_x B_y dz$
+
+If $\theta /= 0$ then we have to tilt the integral and calculate $B_p$ using the expression above.
+
+
+
+
+
+
 {{{
 
@@ -21 +60 @@
 #  *** params ***
 angjet=0.0
-s=math.tan(angjet)
+tt=math.tan(angjet)
+cc=math.cos(angjet)
+ss=math.sin(angjet)
 DefineScalarExpression("angjet", str(angjet))
 xcells=16 #from data
@@ -43 +84 @@
 
 if mode == MODE3D #Create expressions in advance
-     DefineScalarExpression("Bproj", "Bz*cos(angjet)+Bx*sin(angjet)")
-     DefineScalarExpression("I", "fact*(By*By+Bproj*Bproj)")
-     DefineScalarExpression("Q", "fact*(By*By-Bproj*Bproj)")
-     DefineScalarExpression("U", "2.*fact*Bproj*By")
+     DefineScalarExpression("Bproj", "By*cos(angjet)+Bz*sin(angjet)")
+     DefineScalarExpression("I", "fact*(Bx^2+Bproj^2)")
+     DefineScalarExpression("Q", "fact*(Bx^2-Bproj^2)")
+     DefineScalarExpression("U", "2.*fact*Bproj*Bx")
+else if mode == MODE25D
+     DefineScalarExpression("xp", "1.0")
+     DefineScalarExpression("Bzz", "Bz*xp/x")
+     DefineScalarExpression("Bxx", Bz*sqrt(x^2-xp^2)/x")
+     DefineScalarExpression("Bproj", "By*cos(angjet)+Bzz*sin(angjet)")
+     DefineScalarExpression("dzdx", "x/sqrt(x^2-xp^2)")   
+     DefineScalarExpression("I","2*fact*( Bxx^2+Bproj^2) * dzdx")
+     DefineScalarExpression("Q","2*fact*( (Bxx^2-Bproj^2)*dxdz")
+     DefineScalarExpression("U","2*2.*fact*Bxx*Bproj")    
 
 #get data extents
@@ -92 +142 @@
 
 #compute (integral in z)
-yshift=.5*s*(zlim[1]-zlim[0])
+yshift=.5*tt*(zlim[1]-zlim[0])
 
 x=xlim[0]
@@ -99 +149 @@
 
    if mode == MODE25D: #update expressions for integral calculations
-        DefineScalarExpression("I","2*fact*( (Bz*sqrt(x^2-"+str(x)+"^2)/x)^2+By^2) * x/sqrt(x^2-"+str(x)+"^2)")
-        DefineScalarExpression("Q","2*fact*( (Bz*sqrt(x^2-"+str(x)+"^2)/x)^2-By^2) * x/sqrt(x^2-"+str(x)+"^2)")           
-        DefineScalarExpression("U","2*2.*fact*By*Bz")    
+        DefineScalarExpression("xp",str(x))
   
    y=ylim[0]