Aharonov-Bohm radiation

A solenoid oscillating in vacuum will pair produce charged particles due to the Aharonov-Bohm (AB) interaction. We calculate the radiation pattern and power emitted for charged scalar particles. We extend the solenoid analysis to cosmic strings and find enhanced radiation from cusps and kinks on loops. We argue by analogy with the electromagnetic AB interaction that cosmic strings should emit photons due to the gravitational AB interaction of fields in the conical spacetime of a cosmic string. We calculate the emission from a kink and find that it is of similar order as emission from a cusp, but kinks are vastly more numerous than cusps and may provide a more interesting observational signature.

Figure 1

Feynman diagram for pair creation by oscillating solenoid. The solenoid creates an oscillating gauge potential, $A_{\mu }$, while the field strength is always zero outside the solenoid. The time-dependent pure gauge $A_{\mu }$ leads to particle production.

Figure 2

Plot of $J_n(x)/x$ for $n=1$, 2, 3, and 4, where the amplitude of the peak decreases with increasing $n$.

Figure 3

Here we show the radiated power as a function of $\theta$ and ${\theta }^{\prime }$. The top figure is for $n=1$ with $|\mathit{p}|=n\Omega /2=|{\mathit{p}}^{\prime }|$ and the lower figure is for $n=2$. There is maximum radiation along the line $\theta +{\theta }^{\prime }=\pi$, implying back to back emission. For $n=1$, the peaks occur at $\theta =\pi /2$, $3\pi /2$. For $n=2$, they occur at $\theta =\pi /4$, $3\pi /4$, $5\pi /4$, and $7\pi /4$.

Figure 4

$\ln ({\dot{\mathcal{E}}}_n)$ vs $n$ for $\Omega A=0.1$ (lowest curve), 0.5 (middle curve), and 1.0 (top curve).

Figure 5

$\dot{\mathcal{E}}$ vs $\Omega A$ for the oscillating solenoid.

Figure 6

Three snapshots of a degenerate kinky loop.

Figure 7

The plot of $2\pi ({\pi }^{2}L/4ϵ{)}^{2}P(N)$ versus $N$ for the degenerate kinky loop shows $P(N)\propto N$ growth.

Figure 8

$(8\pi L^2/{ϵ}^2){\dot{E}}_n$ versus $n$ for the loop with cusps.

Figure 9

A conical space is obtained by cutting out a wedge from a Euclidean two-dimensional space and identifying the edges. The wave function of a particle that goes around the tip of the cone acquires a phase given by the deficit angle.

Figure 10

Plot of the power radiated $2\pi ({\pi }^{2}L/8\delta {)}^{2}P(N)$ up to some harmonic $N$ for gravitational AB radiation from the square loop, showing the $P(N)\propto N$ growth.