Bremsstrahlung
Angular distribution

The most general formula for radiated power as a function of angle is: d P d Ω = q ¯ 2 4 π c | n ^ × ((n ^ − β) × β ˙) | 2 (1 − n ^ ⋅ β) 5 {\displaystyle {\frac {dP}{d\Omega }}={\frac {{\bar {q}}^{2}}{4\pi c}}{\frac {\left|{\hat {\mathbf {n} }}\times \left(\left({\hat {\mathbf {n} }}-{\boldsymbol {\beta }}\right)\times {\dot {\boldsymbol {\beta }}}\right)\right|^{2}}{\left(1-{\hat {\mathbf {n} }}\cdot {\boldsymbol {\beta }}\right)^{5}}}} where n ^ {\displaystyle {\hat {\mathbf {n} }}} is a unit vector pointing from the particle towards the observer, and d Ω {\displaystyle d\Omega } is an infinitesimal solid angle.

In the case where velocity is parallel to acceleration (for example, linear motion), this simplifies to d P a ∥ v d Ω = q ¯ 2 a 2 4 π c 3 sin 2 θ (1 − β cos θ) 5 {\displaystyle {\frac {dP_{a\parallel v}}{d\Omega }}={\frac {{\bar {q}}^{2}a^{2}}{4\pi c^{3}}}{\frac {\sin ^{2}\theta }{(1-\beta \cos \theta)^{5}}}} where θ {\displaystyle \theta } is the angle between β {\displaystyle {\boldsymbol {\beta }}} and the direction of observation n ^ {\displaystyle {\hat {\mathbf {n} }}}.
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