Compact cyclotron resonance high-power accelerator for electrons

Exact numerical solutions for the single particle equations of motion have revealed conditions for highly nonlinear rapid acceleration near cyclotron resonance for electrons injected into a ${\mathrm{TE}}_{111}$-rotating-mode cylindrical microwave cavity immersed in a uniform axial magnetic field. We dub this the eCRA interaction. Magnitudes of acceleration energy in eCRA are shown to exceed to a large degree the limits for the related cyclotron autoresonance acceleration (CARA) interaction, wherein autoresonance acceleration is sustained for traveling rotating ${\mathrm{TE}}_{11}$-mode waves in a cylindrical waveguide. As with CARA, all injected electrons in an idealized eCRA enjoy equal energy gain without bunching. Injection of high currents that involve heavy beam loading allow acceleration in eCRA to multi-MeV levels for beams with average powers of hundreds of kW and rf-to-beam power efficiencies that exceed 80%. It is shown, to cite one example, that an effective acceleration gradient of over $90\mathrm{MV}/\mathrm{m}$ can be sustained with a maximum cavity surface field of only $40\mathrm{MV}/\mathrm{m}$, when producing a 4.5 MeV, 300 kW average power electron beam, with an rf-to-beam efficiency of about 86%. In that example, the cavity operates at 2.856 GHz, and the cavity’s average surface heating rate is $100\mathrm{W}/{\mathrm{cm}}^2$. Other examples are given for beams with over one MW levels of average power and energies up to about 20 MeV. This paper’s goal is only to elucidate and give examples of the basic mechanism for the strongly nonlinear acceleration that is predicted to occur in eCRA, rather than to present a particular engineered design. Still, the predicted parameters for an idealized eCRA suggest that practical realizations could emerge to satisfy a range of needs for efficient, compact accelerators for industrial, commercial, and national security applications.

Figure 1

Particle orbits within an eCRA cavity. Example (a) is for a cavity with radius $R=6.0\mathrm{cm}$ and length $L=6.113\mathrm{cm}$, showing a nonreflecting orbit; while for (b), $R=7.0\mathrm{cm}$ and $L=5.84\mathrm{cm}$, showing an orbit that reflects within the cavity. Both are for injected particle energies of 100 keV, and for $E_w=100\mathrm{MV}/\mathrm{m}$. In (a) the guide magnetic field $B_o=0.914\mathrm{T}$, while in (b) $B_o=0.650\mathrm{T}$. The electron trajectories are in green (before the cavity), red (in the cavity) and violet (after the cavity). Note that the orbit shown in (a) achieves full acceleration to 10.13 MeV in only about one turn.

Figure 2

Increase in relativistic energy factor $\gamma$ of nonreflected electrons in an eCRA cavity with $R=6.0\mathrm{cm}$, and $L=6.113\mathrm{cm}$, for the indicated values of maximum rf electric field at the wall $E_w$. The electrons enter at $x=y=z=0$, with initial kinetic energy 100 keV. Energy gain is seen to be mainly in the $\sim 3\text{−}\mathrm{cm}$ central region of the cavity where the $E$-fields are strongest; but the nominal acceleration gradient values we cite are equal to the energy gain divided by the full cavity length. See Table 2 for other parameters.

Figure 3

(a) Projection on a plane transverse to the cavity axis over one or more rf periods of the eccentric helical orbit of an accelerated particle. Note the 0.35 cm offset of this helix’s axis from (0,0). (b) Plot of the radial coordinate of a particle along $z$ showing the undulation from its initial radial kick that causes the offset of eccentric helical orbits. (c) Superposition over a full cycle of the loci of orbit intersections where particles intersect a target beyond the cavity. This shows how an eCRA beam is centered on (0,0), how it would scan and deposit its energy uniformly around a circle on a target, and how it remains unbunched.

Figure 4

Behavior of final values of $\gamma$ vs $B_o$ as electrons exit cavities of various radii, with curves labeled according to the cavity radius $R$ in cm. (a) $E_w=20MV/m$ (b) $E_w=50MV/m$ (c) $E_w=100MV/m$ (d) $E_w=200MV/m$. Eneries of accelerated electrons in these examples are between about 2 and 20 MeV.

Figure 5

(a) Final maximum gamma factors vs $E_w$ for various cavity radii; (b) corresponding values of $B_o$.

Figure 6

Quality factor vs radius for ${\mathrm{TE}}_{111}$ copper cavities resonant at 2.856 GHz. Realistic cavities, with beam and coupling apertures, will have lower values.

Figure 7

Values of peak rf power $P_w$ needed to sustain the given values of $E_w$, for a range of cavity radii.

Figure 8

Maximum average power that can be dissipated on ${\mathrm{TE}}_{111}$ cavity walls versus radius of a 2.856 GHz cavity, when the average areal power is $100\mathrm{W}/{\mathrm{cm}}^2$.

Figure 9

Maximum duty factors $\mathrm{\Delta }$ that are consistent with the wall heat load values in Fig. 8.

Figure 10

(a) Average beam power, (b) average beam current, and (c) rf-to-beam efficiency; for eCRA’s at 2.856 GHz operating with peak wall fields of $40\mathrm{MV}/\mathrm{m}$, for three cavity radii. For these cavities, accelerations up to 4.03, 4.36, and 4.58 MeV, respectively, are predicted.

Figure 11

Similar to Fig. 10, except for peak wall fields of $100\mathrm{MV}/\mathrm{m}$. For these cavities, accelerations up to 9.7, 10.2, and 10.7 MeV, respectively, are predicted.