Cyclotron Autoresonance Acceleration Research Articles

Investigation of the collective effects in the cosmic Zevatron based on cyclotron auto-resonance by preliminary particle-in-cell simulations

Cyclotron autoresonance acceleration has been recently advanced as a potential mechanism for accelerating nuclei to ZeV energies (1 ZeV = 1021 eV). All results have been based on single- and many-particle calculations employing analytic solutions to the relativistic equations of motion in the combined magnetic and radiation fields, excluding effects related to the particle-particle interactions. Here, results from preliminary many-particle calculations and preliminary Particle-In-Cell (PIC) simulations, are presented which lend support to the single-particle investigations. Each single-particle result is found to lie well within one standard deviation about the ensemble average obtained from the corresponding many-particle calculation. The PIC simulations show that, even for number densities far exceeding those employed in the non-interacting case, the energy gain drops markedly due to the collective effects, over the first ∼8 mm of the acceleration length. Together with the substantial attenuation, this finding supports the conclusion that the particle-particle interaction effects can be negligibly small over acceleration lengths of typically many kilometers.

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 $90\text{ }\text{ }\mathrm{MV}/\mathrm{m}$ can be sustained with a maximum cavity surface field of only $40\text{ }\text{ }\mathrm{MV}/\mathrm{m}$, 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 $100\text{ }\text{ }\mathrm{W}/{\mathrm{cm}}^{2}$. 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.

Cyclotron auto-resonance for cosmic-ray acceleration to ZeV energies

Equations are derived here for the dynamics of particles undergoing cyclotron autoresonance acceleration in which elliptically-polarized plane-wave radiation fields are employed. The equations are used to study the acceleration of bare atomic nuclei in astrophysical environments by performing single-particle calculations, supported by many-particle simulations. It is shown that the nuclides 1H1, 2He4, 26Fe56, and 28Ni62, can reach ZeV energies in the presence of superintense radiation and megatesla magnetic fields. Nuclides of any species are shown to attain maximum kinetic energy from interaction with an integer number of phase cycles of left circularly-polarized radiation.

A Cosmic Zevatron Based on Cyclotron Auto-resonance

Abstract A Zevatron is an accelerator scheme envisaged to accelerate particles to ZeV energies (1 ZeV = 1021 eV). Schemes, most notably the internal shock model, have been proposed to explain the acceleration of ultra-high-energy cosmic-ray particles that have been sporadically detected reaching Earth since 1962. Here, the cyclotron auto-resonance acceleration (CARA) mechanism is tailored and used to demonstrate the possible acceleration of particles ejected as a result of violent astrophysical processes such as the merger of a binary system or a supernova explosion. Such events result in emission of highly energetic particles and ultra-intense beamed radiation. In the simultaneous presence of a super-strong magnetic field, the condition for cyclotron auto-resonance may be met. Thus CARA can act like a booster for particles pre-accelerated inside their progenitor by shock waves, possibly among other means. As examples, it is shown that nuclei of hydrogen, helium, and iron-56, may reach ZeV energies by CARA, under which conditions the particles, while gyrating around the lines of an ultra-strong magnetic field, also surf on the waves of a super-intense radiation field. When radiation-reaction is taken into account, it is shown that the ZeV energy gained by a particle can fall off by less than an order of -magnitude if the resonance condition is missed by roughly less than 20%.

Feasibility of electron cyclotron autoresonance acceleration by a short terahertz pulse.

A vacuum auto-resonance accelerator scheme for electrons, which employs terahertz radiation and currently available magnetic fields, is suggested. Based on numerical simulations, parameter values, which could make the scheme experimentally feasible, are identified and discussed.

Modeling of electron cyclotron resonance acceleration in a stationary inhomogeneous magnetic field

In this paper, the cyclotron autoresonance acceleration of electrons in a stationary inhomogeneous magnetic field is studied. The trajectory and energy of electrons are found through a numerical solution of the relativistic Newton-Lorentz equation by a finite difference method. The electrons move along a ${\mathrm{TE}}_{112}$ cylinder cavity in a steady-state magnetic field whose axis coincides with the cavity axis. The magnetic field profile is such that it keeps the phase difference between the electric microwave field and the electron velocity vector within the acceleration phase band. The microwaves amplitude of $6\text{ }\text{ }\mathrm{kV}/\mathrm{cm}$ is used for numerical calculations. It is shown that an electron with an initial longitudinal energy of 8 keV can be accelerated up to 260 keV by 2.45 GHz microwaves at a distance of 17 cm.

Cyclotron autoresonance acceleration with seventh harmonic co-generation

The TE/sub 72/ mode in a cylindrical waveguide at frequency 7/spl omega/ has its group velocity /spl upsi//sub gr/ nearly equal to that of the TE/sub 11/ mode at frequency /spl omega/. In consequence, the two modes have nearly equal resonant magnetic fields for strongly coupled interactions at electron cyclotron resonance. This allows coherent radiation in the TE/sub 72/ mode to be generated at 7/spl omega/ as a gyrating electron beam is energized using the TE/sub 11/ mode at frequency /spl omega/ in the same waveguide. It is shown analytically that the electron gyration radius can approach 0.5431 times the waveguide radius during cyclotron autoresonance acceleration, for an axis-encircling beam injected with zero transverse momentum. This fact allows electron acceleration to relativistic energies using the TE/sub 11/ mode to lead to large enough axis-encircling orbit radii for strong coupling with the TE/sub 72/ fields. Results of a particle simulation study are discussed for a 300-kV, 30-A finite-emittance pencil beam injected into a 3.27-cm-radius waveguide, and driven with 20 MW of radio frequency (RF) power at 2.856 GHz. The results show that careful choice of the magnetic field profile, and suppression of the TE/sub 11/ mode after its power is depleted, can allow seventh-harmonic output to reach 10 MW at 20 GHz. Furthermore, it is shown that injection at the input of harmonic power can also benefit co-generation, both increasing seventh-harmonic output up to 16 MW and improving spent beam quality. Higher spent beam quality is advantageous for efficient beam energy recovery.

Efficient Co-Generation of Seventh-Harmonic Radiation in Cyclotron Autoresonance Acceleration.

It is shown that the lowest ${\mathrm{TE}}_{s,l}$ mode in a cylindrical waveguide at frequency $s\ensuremath{\omega}$, with group velocity nearly identical to group velocity for the ${\mathrm{TE}}_{11}$ mode at frequency $\ensuremath{\omega}$, is that with $s\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}7$, $l\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2$. This allows coherent radiation to be generated at the seventh harmonic during electron cyclotron autoresonance acceleration. Conditions are found where such co-generation of 7th harmonic power at 20 GHz is possible with overall efficiency greater than 80%. This mechanism could make possible high efficiency cm-wavelength high power rf sources suitable for driving a future multi-TeV electron-position collider.

Theory of relativistic cyclotron masers.

In this paper we have made an attempt to review the present status of the theory of cyclotron masers with relativistic electron beams. After discussing the basic features of electron-cyclotron radiation under conditions of normal and anomalous Doppler frequency shifts, we consider particle deceleration by a constant amplitude electromagnetic wave in a constant magnetic field using the formalism developed earlier for cyclotron autoresonance acceleration of electrons. An optimal cyclotron resonance mismatch was found that corresponds to the possibility of complete deceleration of relativistic electrons. Then, interaction of relativistic electrons with resonator fields is considered and the efficiency increase due to electron prebunching is demonstrated in a simple model. Since an efficient interaction of relativistic electrons with the large amplitude electromagnetic field of a resonator occurs at a short distance, where electrons make a small number of electron orbits, the issue of the simultaneous interaction of electrons with the field at several cyclotron harmonics is discussed. Finally, we consider deceleration of a prebunched electron beam by a traveling electromagnetic wave in a tapered magnetic field. This simple modeling is illustrated with a number of simulations of relativistic gyroklystrons and gyrotwistrons (gyrodevices in which the bunching cavity of the gyroklystron is combined with the output waveguide of the gyro-traveling-wave-tube).

Energy limit in cyclotron autoresonance acceleration.

A multimegawatt gyroharmonic converter depends critically on the parameters of a spatiotemporally modulated gyrating electron beam prepared using a cyclotron autoresonance accelerator (CARA). This paper extends a prior analysis of CARA [B. Hafizi, P. Sprangle, and J. L. Hirshfield, Phys. Rev. E 50, 3077 (1994)] to identify an approximate constant of the motion and, therefore, to give limits to the beam energy from CARA that can be utilized in a harmonic converter. It is also shown that particles are strongly phase trapped during acceleration in CARA and thus are insensitive to deviations from exact autoresonance. This fact could simplify construction of the up-tapered guide magnetic field in the device and augurs well for production of high-quality multimegawatt beams using CARA.