Focusing Of Charged Particle Beams Research Articles

Half-wavelength velocity bunching: non-adiabatic temporal focusing of charged particle beams

X-ray free-electron lasers (XFELs) and megaelectronvolt ultrafast electron diffractometers (MeV UEDs) are revolutionary scientific instruments that allow visualizing the dynamics of elementary excitations in a wide range of systems from atoms and molecules to phonons, magnons and plasmons. Femtosecond (fs) electron beams are at the heart of XFELs and MeV UEDs, and the formation of fs electron beams with ultrahigh brightness is the subject of active research. We report an interesting regime of non-adiabatic temporal compression of electron beams by two orders of magnitude. Via analytical calculations and numerical simulations, we show that few MeV electron bunches can be trapped and compressed by a strong electromagnetic field within a half of the field wavelength. Furthermore, in a multi-cell accelerating cavity, the bunch is first compressed and then accelerated, thus allowing one to preserve very short bunch duration. For example, a 3 ps 16 pC 1 MeV electron bunch is compressed to 21 fs rms and accelerated to 12 MeV in a TESLA superconducting cavity. Another example is the production of 1.2 fs 16 fC 3.3 MeV bunches with a coherence length of 20 nm and and an energy spread less than 3 keV. The discovered mechanism of compression, which is another mode of velocity bunching, opens the door for obtaining very high electron brightness.

Relativistic nonlinear whistler waves in cold magnetized plasmas

Starting from the Vlasov-Maxwell equations describing the dynamics of various species in a quasi-neutral plasma immersed in an external solenoidal magnetic field and utilizing a technique known as the hydrodynamic substitution, a relativistic hydrodynamic system of equations governing the dynamics of various species has been obtained. Based on the method of multiple scales, a system comprising three nonlinear Schrodinger equation for the transverse envelopes of the three basic whistler modes, has been derived. Using the method of formal series of Dubois-Violette, a traveling wave solution of the derived set of coupled nonlinear Schrodinger equations in both the relativistic and the non relativistic case has been obtained. An intriguing feature of our description is that whistler waves do not perturb the initial uniform density of plasma electrons. The plasma response to the induced whistler waves consists in transverse velocity redistribution, which follows exactly the behaviour of the electromagnetic whistlers. This property may have an important application for transverse focusing of charged particle beams in future laser plasma accelerators. Yet another interesting peculiarity are the selection rules governing the nonlinear mode coupling. According to these rules self coupling between modes in the non relativistic regime is absent, which is a direct consequence of the vector character of the interaction governed by the Lorentz force.

Emittance Preservation in an Aberration-Free Active Plasma Lens

Active plasma lensing is a compact technology for strong focusing of charged particle beams, which has gained considerable interest for use in novel accelerator schemes. While providing kT/m focusing gradients, active plasma lenses can have aberrations caused by a radially nonuniform plasma temperature profile, leading to degradation of the beam quality. We present the first direct measurement of this aberration, consistent with theory, and show that it can be fully suppressed by changing from a light gas species (helium) to a heavier gas species (argon). Based on this result, we demonstrate emittance preservation for an electron beam focused by an argon-filled active plasma lens.

Electrostatic Spectrograph for Different Ranges of Simultaneously Recorded Energies with a Discrete Combined External Electrode

We propose and study numerically a large-aperture electrostatic spectrograph consisting of the two coaxial electrodes, a cone-cylindrical electrode separated into several segments, and a small cylindrical electrode. The supply voltages providing sharp focusing of charged particle beams in the initial region of the spectrum for different ranges of simultaneously detected energies Emax/Emin = (25–100) are determined. Electron- optical parameters of the spectrograph in four energy ranges are calculated, with the electrical similarity principle being used for charged particles of medium and high energies. The resolution of the spectrograph for medium and high energies, E = (0.1–1)Emax, is equal to (5–3) × 10–3. For small energies, E = (0.01–0.1)Emax, the resolution worsens and varies within the (0.6–1.6) × 10–2 range as the range of simultaneously recorded energies increases.

Amplification due to two-stream instability of self-electric and magnetic fields of an ion beam propagating in background plasma

Propagation of charged particle beams in background plasma as a method of space charge neutralization has been shown to achieve a high degree of charge and current neutralization and therefore enables nearly ballistic propagation and focusing of charged particle beams. Correspondingly, the use of plasmas for propagation of charged particle beams has important applications for transport and focusing of intense particle beams in inertial fusion and high energy density laboratory plasma physics. However, the streaming of beam ions through a background plasma can lead to the development of two-stream instability between the beam ions and the plasma electrons. The beam electric and magnetic fields enhanced by the two-stream instability can lead to defocusing of the ion beam. Using particle-in-cell simulations, we study the scaling of the instability-driven self-electromagnetic fields and consequent defocusing forces with the background plasma density and beam ion mass. We identify plasma parameters where the defocusing forces can be reduced.

Understanding the focusing of charged particle beams in a solenoid magnetic field

The focusing of a charged particle beam in a solenoid is typically explained by invoking the concept of a Larmour frame and using Busch’s theorem. Often, there is some confusion about how a uniform magnetic field of a long solenoid focuses the electron beam because it is generally understood that a uniform magnetic field can only guide charged particles. We perform a simple analysis of the dynamics of a charged particle beam in a solenoid and emphasize an intuitive understanding of some of the interesting features.

A new derivation of the plasma susceptibility tensor for a hot magnetized plasma without infinite sums of products of Bessel functions

The susceptibility tensor of a hot, magnetized plasma is conventionally expressed in terms of infinite sums of products of Bessel functions. For applications where the particle’s gyroradius is larger than the wavelength, such as alpha particle dynamics interacting with lower-hybrid waves, and the focusing of charged particle beams using a solenoidal field, the infinite sums converge slowly. In this paper, a new derivation of the plasma susceptibility tensor is presented which exploits a symmetry in the particle’s orbit to simplify the integration along the unperturbed trajectories. As a consequence, the infinite sums appearing in the conventional expression are replaced by definite double integrals over one gyroperiod, and the cyclotron resonances of all orders are captured by a single term. Furthermore, the double integrals can be carried out and expressed in terms of Bessel functions of complex order, in agreement with expressions deduced previously using the Newburger sum rule. From this new formulation, it is straightforward to derive the asymptotic form of the full hot plasma susceptibility tensor for a gyrotropic but otherwise arbitrary plasma distribution in the large gyroradius limit. These results are of more general importance in the numerical evaluation of the plasma susceptibility tensor. Instead of using the infinite sums occurring in the conventional expression, it is only necessary to evaluate the Bessel functions once according to the new expression, which has significant advantages, especially when the particle’s gyroradius is large and the conventional infinite sums converge slowly. Depending on the size of the gyroradius, the computational saving enabled by this representation can be several orders-of-magnitude.

The charged particle time-of-flight and space focusing in a two-dimensional electrostatic field

Unknown earlier regularities of space and time-of-flight focusing of charged particle beams in electrostatic fields with a mid-plane have been revealed. The conditions of both space and time-of-flight high quality focusing are determined.

Synthesis of focusing-and-deflection columns

Szilagyi and Szep have demonstrated that focusing lenses of high performances can be constructed from a column of circular plate electrodes. Later, Szilagyi modified that system to include dipole, quadrupole, and octupole components by partitioning each plate into eight equal sectors. It has already been shown that the additional quadrupole components can indeed bring about substantial improvements in the focusing of charged particle beams. In this article, that design procedure is expanded to construct columns capable of both focusing and deflecting particle beams by just introducing additional dipole components. In this new design, the geometry of the system remains unchanged. The only extra complication is the demand for more individual controls of the sector voltages. Two sample designs, one for negative ions and one for electrons, are presented showing that in both cases a ±2.3 mrad diverging beam can be focused down to a spot of less than 50 nm in radius over a scanning circular area of radius 0.25 mm. The details of the two systems are given in Sec. IV along with the source conditions. The performance of the negative ion system is found to be comparable to the published data. For the relativistic electron system, the interaction of individual components to reduce various aberrations is investigated.

Permanent multipole magnetic fields stored in superconductors

Hollow superconducting cylinders of Pb, Nb, and Nb3Sn were used to permanently store dipole, quadrupole, and sextupole magnetic fields with high fidelity to the original fields. Fields were trapped transversely to the axes of solid, hollow, and split hollow cylinders. This experimental demonstration indicates that it should be possible to store any multipole magnetic field configuration by this method. Important benefits should accrue to technologies dealing with the focusing of charged particle beams, such as accelerators, electron microscopes, etc. Use of field trapping permits determination of the fluxoid pinning force.