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## Homework Statement

An electron moves in a helix : [tex]\vec{r}(t)=v_{z}t \hat{z}+a e^{i\omega_{0}t}(\hat{x}-i\hat{y})[/tex], where [tex]a[/tex] is the radius of the helix and [tex]v_{z}[/tex] the relativistic z-component of the velocity.

1) Find the position vector of the electron in a system of reference that is moving with velocity [tex]v_{z}\hat{z}[/tex]

2) Find the central frequency of radiation that the electron emits in the [tex]\hat{z}[/tex] direction in the laboratory reference frame.

3)Calculate the angular distribution of the power of radiation, [tex]\frac{dP(t')}{d\Omega}[/tex]

## Homework Equations

Jackson 3rd edition, chapter 14 (par. 14.4)

## The Attempt at a Solution

1) is easy, just a lorentz transformation to find [tex]\vec{r}'(t')[/tex]. It turns out that in the moving frame [tex]\vec{r}'(t')[/tex] has no z-component. So in that frame it actually moves in a circle rather than a helix.

For 2)I have no idea.

3)I can maybe calculate [tex]\frac{dP(t')}{d\Omega}[/tex] from equation 14.38 but I am not sure

Any ideas? Especially for 2)...