Can Someone explain Why we integrate over 4[tex]\pi[/tex]? What allows

  • Thread starter candice_84
  • Start date
  • #1
45
0
Can Someone explain Why we integrate over 4[tex]\pi[/tex]? What allows us to get rid of Omega?
 

Attachments

  • 1.jpg
    1.jpg
    7.6 KB · Views: 303
Last edited:

Answers and Replies

  • #2
Astronuc
Staff Emeritus
Science Advisor
19,221
2,685


One is simply integration over all 'directions'. 4π is just the total solid angle, which represents all directions/orientations.
 
  • #3
45
0


2pi = 360 which is enough.
 
Last edited:
  • #4
Astronuc
Staff Emeritus
Science Advisor
19,221
2,685


2pi = 360 which is enough.

2 pi in 2D, not 3D.

In 3D, 2 pi is half the solid angle encompassed by a sphere, i.e. hemisphere.

Think - the area of a sphere is 4pi r2, where r is the radius.

Note, when one refers to
[tex]\phi(r,E,\vec{\Omega})[/tex]
one is referring to the angular flux in n/cm2-s-(unit E)-steradian.

Integrating over the solid angle gives the 'scalar' flux.

http://en.wikipedia.org/wiki/Neutron_transport
 
Last edited:
  • #5
45
0


solid angle is a volume?
 
  • #6
Astronuc
Staff Emeritus
Science Advisor
19,221
2,685


solid angle is a volume?
No solid angle is the solid angle, like angle is angle in 2D. The 4π (steradians) solid angle is the 3D analog to 2π radians in 2D.

The total solid angle would be the area of a sphere divided by r2, i.e. A/r2 = 4πr2/r2 = 4π, just like 2π = circumference (2π r) of the circle divided by r.

http://en.wikipedia.org/wiki/Steradian
http://en.wikipedia.org/wiki/Solid_angle

http://mathworld.wolfram.com/SolidAngle.html
http://mathworld.wolfram.com/Radian.html
http://mathworld.wolfram.com/Angle.html
 
  • #7
45
0


This integration is only correct if we assume neutrons are produce and move uniformly. Its better to not convert it to scalar format, am i right?
 

Related Threads on Can Someone explain Why we integrate over 4[tex]\pi[/tex]? What allows

Replies
43
Views
6K
  • Last Post
Replies
4
Views
1K
Replies
3
Views
4K
Replies
70
Views
6K
Replies
2
Views
1K
Replies
7
Views
2K
Top