Analytic calculation of the electric field of a coherent THz pulse

Accelerators can serve as sources for intense THz radiation by producing sub-ps long electron bunches, which generate synchrotron radiation coherently in the THz regime. In this paper, we present an analytic method to calculate the electric field pulse emitted by an electron bunch with arbitrary bunch shape. Our method is applied to a Gaussian bunch as well as a complex bunch profile resulting from a nonlinear beam dynamics simulation.

Figure 1

Time dependence of the electric field $E$, coherently emitted by a Gaussian bunch with length $\sigma$ according to Eq. (9). The parameters are $Q=100\mathrm{pC}$, $R=1\mathrm{m}$, $\rho =1.1\mathrm{m}$, and ${\sigma }_b=50\mathrm{fs}$. For $\varphi =0$ (continuous) we get a symmetric so-called half-cycle pulse whereas $\varphi =65°$ (dashed) and $\varphi =325°$ (dotted) yield single-cycle pulses with minima at $t>0$ and $t<0$, respectively.

Figure 2

Electric field of a THz pulse emitted by a 100 pC Gaussian bunch of width $\sigma =50\mathrm{fs}$ calculated according to Eq. (9) (continuous) and based on the cubic spline interpolation (points). The parameters were $R=1\mathrm{m}$, $\rho =1\mathrm{m}$, and $\varphi =45°$.

Figure 3

(a) Simulated longitudinal charge profile of a 100 pC bunch at FLUTE. Points are simulated data, while the continuous line is a fit of the data to a sum of four Gaussians. (b) Calculated electric field $E$ based on the multi-Gaussian fit and Eq. (9) (continuous) as well as the spline interpolation and Eq. (19) (points). Notice how, for the phase $\varphi =0°$ used here, each pulse shape follows its underlying temporal charge profile.

Figure 4

Calculated electric field $E$ based on the multi-Gaussian fit and Eq. (9) (continuous) as well as the spline interpolation and Eq. (19) (points) for the longitudinal charge profile of Fig. 3 using $\varphi =65°$ (a) and $\varphi =325°$ (b).