Presence Of Self-fields Research Articles

Optimization of flat to round transformers with self-fields using adjoint techniques

A continuous system of moment equations is introduced that models the transverse dynamics of a beam of charged particles as it passes through an arbitrary lattice of quadrupoles and solenoids in the presence of self-fields. Then, figures of merit are introduced specifying system characteristics to be optimized. The resulting model is used to optimize the parameters of the lattice elements of a flat to round transformer with self-fields, as could be applied in electron cooling. Results are shown for a case of no self-fields and two cases with self-fields. The optimization is based on a gradient descent algorithm in which the gradient is calculated using adjoint methods that prove to be very computationally efficient. Two figures of merit are studied and compared: one emphasizing radial force balance in the solenoid, the other emphasizing minimization of transverse beam energy in the solenoid.

Dispersion relation of a two-beam free electron laser with realistic helical wiggler and ion channel guiding in the presence of self-fields

Dispersion relation of a two-beam free electron laser with realistic helical wiggler and ion channel guiding in the presence of self-fields

Propagation and Interaction of Electrostatic and Electromagnetic Waves in Two Stream Free Electron Laser in the Presence of Self-Fields

Propagation and Interaction of Electrostatic and Electromagnetic Waves in Two Stream Free Electron Laser in the Presence of Self-Fields

Erratum to: Effects of electron beam velocity spread, temperature, and self-fields on dispersion relation and growth rate in a Cherenkov radiation

We study the effects of electron beam velocity spread, temperature, and self-fields on dispersion relation and growth rate in a Cherenkov radiation when an axial magnetic field is present. A generalized dispersion relation is derived and shown that in addition to cyclotron, FEL, and beam modes there are two other modes which are induced by thermal velocity of electron beam. For cyclotron mode, the effects of electron beam self-fields on the growth rate are investigated and shown that the growth rate in the presence of self-fields has a maximum value which is considerably greater than the saturation value of growth rate in the absence of self-fields. The optimum value of axial magnetic field at which the maximum growth can take place is determined for different electron beam densities. Then the effects of electron beam velocity spread and temperature on growth rate are studied and it is found that the electron beam temperature causes an increment in growth rate, while the velocity spread of electron beam has an opposite effect.

Effects of electron beam velocity spread, temperature, and self-fields on dispersion relation and growth rate for a Cherenkov radiation

We study the effects of electron beam velocity spread, temperature, and self-fields on dispersion relation and growth rate in a Cherenkov radiation when an axial magnetic field is present. A generalized dispersion relation is derived and shown that in addition to cyclotron, FEL, and beam modes there are two other modes which are induced by thermal velocity of electron beam. For cyclotron mode, the effects of electron beam self-fields on the growth rate are investigated and shown that the growth rate in the presence of self-fields has a maximum value which is considerably greater than the saturation value of growth rate in the absence of self-fields. The optimum value of axial magnetic field at which the maximum growth can take place is determined for different electron beam densities. Then the effects of electron beam velocity spread and temperature on growth rate are studied and it is found that the electron beam temperature causes an increment in growth rate, while the velocity spread of electron beam has an opposite effect.

Steady-state electron trajectories in a free electron laser with ion-channel and axial magnetic field in the presence of self-fields

A theory of self-fields in a one-dimensional helical wiggler free electron laser with ion-channel guiding and axial magnetic field is presented. The steady-state orbits under the influence of self-field are derived and discussed. The Φ function that determines the rate of change of axial velocity with energy is derived. The numerical results show the effects of self-fields and the two electron-beams guiding devices (ion-channel and axial magnetic field) on the trajectories when used separately and simultaneously. The study shows that new unstable orbits, in the first part of the group I and II orbits, are found. A detailed stability analysis of orbits is presented.

Dispersion relation and growth rate in a Cherenkov free electron laser: Finite axial magnetic field

A theoretical analysis is presented for dispersion relation and growth rate in a Cherenkov free electron laser with finite axial magnetic field. It is shown that the growth rate and the resonance frequency of Cherenkov free electron laser increase with increasing axial magnetic field for low axial magnetic fields, while for high axial magnetic fields, they go to a saturation value. The growth rate and resonance frequency saturation values are exactly the same as those for infinite axial magnetic field approximation. The effects of electron beam self-fields on growth rate are investigated, and it is shown that the growth rate decreases in the presence of self-fields. It is found that there is an optimum value for electron beam density and Lorentz relativistic factor at which the maximum growth rate can take place. Also, the effects of velocity spread of electron beam are studied and it is found that the growth rate decreases due to the electron velocity spread.

Influence of wall impedance and self-fields on the cyclotron maser instability

The compound influence of wall impedance and self-fields on the cyclotron maser instability is investigated for a hollow electron beam. A stability analysis is carried out using the linearized Vlasov–Maxwell equations, under the assumption that the beam thickness is small compared to the beam radius. A dispersion relation is derived and solved numerically to study the effects of the wall impedance and self-fields on the cyclotron maser instability. These effects lead to the elliptical motion of the equilibrium configuration. The growth rate decreases due to the wall resistivity and self-fields. It has been shown that the interaction between the self-field and impedance effects is in the lower reduction in the growth rate when they are both present compared to their separate effects added together. The instability bandwidth increases due to the wall impedance and decreases due to the self fields. In the presence of self-fields, a very small increase in the wall impedance causes an increase in the instability bandwidth. This shows that the widening effect of the bandwidth due to the wall impedance is dominant and prevails over the narrowing effect of the self-field.

Self-fields effects on gain in a free-electron laser with helical wiggler and axial magnetic field

A theory for gain in a free-electron laser with helical wiggler and axial magnetic field in the presence of self-fields is presented. It is found that for group I orbits, gain decrement is obtained relative to the absence of the self-fields, while for group II orbit gain enhancement is obtained. The gain decrement and enhancement are due to the diamagnetic and paramagnetic effects of the self-magnetic field, respectively.

Electron beam equilibria with self-fields for a free electron laser with a planar wiggler

A general formalism for non-neutral cold relativistic planar steady flows is developed and applied to the study of the equilibrium of a sheet electron beam in a planar wiggler free electron laser. The full transverse dependence of the wiggler field as well as the equilibrium self-fields of the beam are included. In particular, the betatron oscillations in the presence of self-fields are studied. For a thick beam equilibrium with a particular density profile it is shown that the betatron oscillations are eliminated. For a thin beam configuration the paraxial approximation is employed and it is also shown that for some critical density there are no betatron oscillations. If the density is larger than this critical density the beam oscillates with the betatron frequency but there are no trajectory crossings and the beam preserves its cold fluid nature. The single-particle equations of motion are also considered in the presence of both planar wiggler and planar self-fields. It is shown that in some cases the particles oscillate with a reduced betatron frequency, in contrast to the previous case of cold fluid motion where the self-fields do not change the betatron frequency. For the study of the betatron oscillations in the thick beam equilibrium a two-space scale method is employed. For the thin beam within the paraxial approximation the Floquet theory for equations with periodic coefficients is used.

Exact longitudinal equilibrium distribution of stored electrons in the presence of self-fields

The longitudinal equilibrium distribution of electrons stored in a ring is computed in the general case of a nonlinear accelerating field. From this is derived an equation which gives the exact longitudinal density in the presence of longitudinal fields generated by the circulating particles. A method for solving numerically this equation is given and the exact solution is compared to the lowest-approximation solution when self-fields are proportional to the derivative of the bunch density.