I don't know about the physics of it, but I think the warp field should be expansive say about 1 million km in radius. The warp drive pushes everything within that sphere at that warp speed. Warp factors should be in tenths following the Star Trek tradition and using a tangential scale for speed. Here is an example:
Warp Factor --- Velocity
0.1 = tan(4.5)- 0.0787 c
0.2 = tan(9)--- 0.158 c
0.3 = tan(13.5) 0.240 c
0.4 = tan(18)-- 0.325 c
0.5 = tan(22.5) 0.414 c
0.6 = tan(27)-- 0.510 c
0.7 = tan(31.5) 0.613 c
0.8 = tan(36)-- 0.727 c
0.9 = tan(40.5) 0.854 c
1.0 = tan(45)-- 1.00 c
1.1 = tan(47.3) 1.08 c
1.2 = tan(49.5) 1.17 c
1.4 = tan(54)-- 1.37 c
1.6 = tan(58.5) 1.63 c
1.8 = tan(63)-- 1.96 c
2.0 = tan(67.5) 2.41 c
2.4 = tan(72)-- 3.08 c
2.8 = tan(76.5) 4.17 c
3.0 = tan(78.8) 5.03 c
3.5 = tan(81.6) 6.74 c
4.0 = tan(84.4) 10.2 c
5.0 = tan(45+45/2+45/4+45/8+45/16) = 20.4 c
6.0 = tan(45+45/2+45/4+45/8+45/16+45/32) = 40.7 c
7.0 = tan(45+45/2+45/4+45/8+45/16+45/32+45/64) = 81.5 c
8.0 = tan(45+45/2+45/4+45/8+45/16+45/32+45/64+45/128) = 163 c
9.0 = 326 c
10.0 = 652 c
Well you should get the picture. The tenths warp factors are the tangent of tenth intervals of the angular distance between the previous and next interger warp factor. There are energy values associated with each warp factor. The energy value is one tenth the value of the rest energy of all the mass within the warp field multiplied by the warp factor.
Warp Factor --- Velocity
0.1 = tan(4.5)- 0.0787 c
0.2 = tan(9)--- 0.158 c
0.3 = tan(13.5) 0.240 c
0.4 = tan(18)-- 0.325 c
0.5 = tan(22.5) 0.414 c
0.6 = tan(27)-- 0.510 c
0.7 = tan(31.5) 0.613 c
0.8 = tan(36)-- 0.727 c
0.9 = tan(40.5) 0.854 c
1.0 = tan(45)-- 1.00 c
1.1 = tan(47.3) 1.08 c
1.2 = tan(49.5) 1.17 c
1.4 = tan(54)-- 1.37 c
1.6 = tan(58.5) 1.63 c
1.8 = tan(63)-- 1.96 c
2.0 = tan(67.5) 2.41 c
2.4 = tan(72)-- 3.08 c
2.8 = tan(76.5) 4.17 c
3.0 = tan(78.8) 5.03 c
3.5 = tan(81.6) 6.74 c
4.0 = tan(84.4) 10.2 c
5.0 = tan(45+45/2+45/4+45/8+45/16) = 20.4 c
6.0 = tan(45+45/2+45/4+45/8+45/16+45/32) = 40.7 c
7.0 = tan(45+45/2+45/4+45/8+45/16+45/32+45/64) = 81.5 c
8.0 = tan(45+45/2+45/4+45/8+45/16+45/32+45/64+45/128) = 163 c
9.0 = 326 c
10.0 = 652 c
Well you should get the picture. The tenths warp factors are the tangent of tenth intervals of the angular distance between the previous and next interger warp factor. There are energy values associated with each warp factor. The energy value is one tenth the value of the rest energy of all the mass within the warp field multiplied by the warp factor.