Compression of a photoinjector electron bunch in the negative-mass undulator

The use of the “negative mass” regime provides stabilization of longitudinal size of dense photoinjector electron bunches moving through a long undulator. This allows one to increase significantly the power capabilities of a terahertz source based on coherent spontaneous emission from a short bunch. However, such type of emission is produced if the bunch length is comparable with the radiation wavelength. This work discusses the use of the negative mass regime to provide effective compression of dense bunches down to “terahertz” lengths.

Figure 1

Schematic of a rf source based on spontaneous coherent emission from short electron bunches, which includes compression and radiation sections.

Figure 2

(a) Electron bunch moving in a helical undulator with guiding magnetic field. (b) The model of a bunch in the form of a set of charged pancakes. (c) Electric field acting from the jth pancake to the ith one.

Figure 3

The model of an electron bunch consisting of two particles. (a) Coulomb repulsion of the two particles in the positive-mass regime. (b) Typical dependence of the oscillatory (undulator) velocity of a particle on the cyclotron frequency. (c) Coulomb attraction of the two particles in the negative-mass regime.

Figure 4

The model of an electron bunch consisting of two particles. Phase plane describing the evolution of the bunch in the negative-mass undulator, as well as axial positions and energies of the two electrons at different moments of the time, including the initial state (A) and the point of the maximal axial compression (B).

Figure 5

The model of an electron bunch consisting of two particles. Phase planes describing the evolution of the bunch in the negative-mass undulator at different factors of the transverse inhomogeneity $r$.

Figure 6

Different motion of two pairs of electrons, namely, the pair of particles initially placed on the edges of the bunch and a pair of electrons initially placed inside the bunch: (a) initial state, (b) the “meeting point” of the inner pair, and (c) the meeting point of the two edge particles.

Figure 7

Minimal compression factors $l/l_0$ (a) and lengths of the compressing undulator (b) versus the normalized difference between undulator and cyclotron frequencies, $\mathrm{\Delta }$, for electron bunches with initial lengths, $l_0=0.01$, 0.5 and 1 mm.

Figure 8

Dynamics of the electron bunch with an initial length of 0.1 mm moving through a negative-mass undulator ($\mathrm{\Delta }=-0.4$). Effective bunch length normalized to the initial value, $l/l_0$, versus the axial coordinate of the bunch, as well as distributions of electrons on the phase planes (energy/axial position) at different stages of the bunch motion.

Figure 9

Dynamics of the electron bunch with an initial length of 1 mm moving through a negative-mass undulator ($\mathrm{\Delta }=-0.4$). Effective bunch length normalized to the initial value, $l/l_0$, versus the axial coordinate of the bunch, as well as distributions of electrons on the phase planes (energy/axial position) at different stages of the bunch motion.

Figure 10

Long-length dynamic of the electron bunch with an initial length of 1 mm moving through a negative-mass undulator at various mismatches between undulator and cyclotron frequencies, (a) $\mathrm{\Delta }=-0.55$, (b) $\mathrm{\Delta }=-0.48$, and (c) $\mathrm{\Delta }=-0.46$. Axial positions of different particles with respect to the averaged center of the bunch, $z_{\mathrm{j}}-⟨z_{\mathrm{j}}⟩$, versus the current axial coordinate.