Changes between Version 9 and Version 10 of u/erica/d

Timestamp:

12/05/15 14:42:24 (9 years ago)

Author:

Erica Kaminski

Comment:

—

u/erica/d

@@ -47 +47 @@
 7. as far as the ram pressure pushing this ring out, we assume the velocity of the ejecta is a constant with radius, and only the density is decreasing by geometrical dilution. 
 8. we take the ram pressure of the ejecta to be the incoming ram pressure. this is a reasonable approximation as the shocked sound speed should be of order the incoming velocity.
+9. we consider the ring to be formed from a spherical distribution of field lines centered on the collision region. thus, the radius of curvature is just r, and the thermal pressure gradient is along r, but perpendicular to the field directly above the collision region.
 
-This gives:
+This gives the following momentum equation for the ring (i.e. for [[latex($r_i < r < r_o$)]]):
 
 [[latex($0 = -\bold{\nabla}(\frac{B^2}{2 \mu}) + \frac{B^2}{\mu} \frac{\hat{\bold{n}}}{R_c}$)]]