Express gradB drift in full B

henry2004y · Dec 8, 2023 · b3169d9 · b3169d9
1 parent 470ba84
commit b3169d9
Showing 1 changed file with 4 additions and 1 deletion.
diff --git a/contents/single.qmd b/contents/single.qmd
@@ -813,7 +813,10 @@ Nonuniform magnetic field:
 
 Grad-B:
 $$
-\mathbf{v}_{\nabla B} = \pm \frac{1}{2}v_\perp r_L\frac{\mathbf{B}\times\nabla B}{B^2}
+\begin{aligned}
+\mathbf{v}_{\nabla B} &= \pm \frac{1}{2}v_\perp r_L\frac{\mathbf{B}\times\nabla B}{B^2} \\
+&=\frac{mv_\perp^2}{2qB^3}\mathbf{B}\times\nabla B
+\end{aligned}
 $$ {#eq-gc-drift-gradB}
 
 Curvature drift: