Confinement Of Charged Particles Research Articles

Thrust Generation Through a Collimated Electron Beam in a Magnetic Mirror and its Possible Applications in Plasma Thrusters

In this article, we apply some basic concepts of electric thrusters, using Monte Carlo simulations. One such concept is the thrust, which we calculate for the simulated case of a simple thruster, consisting of two stages. The goal is to study the thrust in a magnetic bottle as a function of the collimation of an assembly of particles. In the first stage, a voltage applied between a pair of electrodes accelerates the particles. We perform simulations of the behavior of the assembly of charged particles. A normal distribution is used for the initial velocities of the assembly, with a given standard deviation. The resulting velocity distribution and its dependence on the applied voltage are analyzed. Further, the set of particles, whose pitch angles follow a normal distribution with a given standard deviation, enters a magnetic bottle where it is collimated to reduce its dispersion upon the exit of the thruster. In this second stage, we study the conditions for which the collimation produced, by the magnetic bottle, leads to the least thrust reduction. For the simulations, we assume electrons; However, the concepts apply to any charged particle species. The simulations show that the standard deviation of the pitch angle distribution has an important influence on the confinement of charged particles and on the thrust that can be generated when collimating the particle beam in a magnetic bottle.

Charged particle reflection in a magnetic mirror

We study the reflection of electrons in a magnetic field mirror. It is a field with a gradient from a lowest value B0 to a largest one Bm. With this purpose, Montecarlo simulations are made. We use a number of 5,000 particles with random pitch angles. The frequency distribution of these random values follows a Gaussian distribution centered at \theta = 0 and with standard deviation \sigma. Various values of \sigma and also different values of the B0 /Bm ratio are used in the simulations. The simulations show that \sigma has an important influence on the confinement of charged particles, for the different B0 /Bm ratios here studied. However, the percent of reflected particles differs from a B0 /Bm ratio to another in the whole range of \sigma, although for \sigma = 10 the differences between different ratios are small (<5%). The number of reflected particles increases very rapidly with \sigma, in the range of 10° to 40°. For the \sigma range from 20° to 40°, the percent of reflected particles is \leq 20% larger for B0 /Bm = 0.10 than for the 0.55 ratio.

Effect of discreteness and misalignment on magnetic field and charged particle confinement in CFQS quasi-axisymmetric stellarator

The Chinese first quasi-axisymmetric stellarator (CFQS), which will be the first quasi-axisymmetric (QA) stellarator in the world, is now under construction. The primary task of the CFQS project is to realize a QA configuration and to examine its physical properties. Based on this task, two important issues were investigated in this work in order to estimate the robustness of the CFQS design from a physical perspective. One was the toroidal field (TF) ripple due to the discreteness of modular coils (MCs) which could potentially degrade the charged particle confinement in the CFQS configuration. The other was a possible MC misalignment in the assembly that would affect the magnetic field and charged particle confinement in the CFQS. Moreover, since the stellarator symmetry might be broken by the MC misalignment, such a case was also investigated in this work. By performing a magnetic field line tracing and charged particle orbit tracing calculation, it was found that the TF ripple does not affect the confinement property significantly and the magnetohydrodynamics equilibrium was robust against possible MC misalignments. These results are helpful in defining the reasonable tolerance of assembly accuracy.

Confinement of charged particles and non-neutral plasma in a magnetic mirror

Confinement of charged particles and non-neutral plasma in a magnetic mirror

Magnetic Fields with Precise Quasisymmetry for Plasma Confinement.

Quasisymmetry is an unusual symmetry that can be present in toroidal magnetic fields, enabling the confinement of charged particles and plasma. Here it is shown that both quasiaxisymmetry and quasihelical symmetry can be achieved to a much higher precision than previously thought over a significant volume, resulting in exceptional confinement. For a 1Tesla mean field far from axisymmetry (vacuum rotational transform >0.4), symmetry-breaking mode amplitudes throughout a volume of aspect ratio 6 can be made as small as the typical ∼50 μT geomagnetic field.

Helicon plasma in a magnetic shuttle

The definition of a magnetic shuttle is introduced to describe the magnetic space enclosed by two magnetic mirrors with the same field direction and high mirror ratio. Helicon plasma immersed in such a magnetic shuttle (mirror ratio 5) that can provide the confinement of charged particles is modeled using an electromagnetic solver. The perpendicular structure of the wave field along this shuttle is given in terms of stream vector plots, showing a significant change from midplane to ending throats, and the vector field rotates and forms a circular layer that separates the plasma column radially into core and edge regions near the throats. The influences of the driving frequency (f = 6.78 MHz–40.68 MHz), plasma density (nemax = 1016 m−3 to 1019 m−3), and field strength (B0max = 0.017 T–1.7 T) on the wave field structure and power absorption are computed in detail. It is found that the wave energy and power absorption decrease for increased driving frequency and reduced field strength and increase significantly when the plasma density is above a certain value. The axial standing-wave feature always exists, due to the interference between forward and reflected waves from ending magnetic mirrors. Distributions of wave energy density and power absorption density all show a shrinking feature from midplane to ending throats, which is consistent with the nature of the helicon mode that propagates along field lines. Theoretical analysis based on a simple magnetic shuttle and the governing equation of helicon waves shows consistency with computed results and previous studies. This hypothetical work is a valuable to guide the helicon physics prototype experiment, which is designed for the fundamental wave–particle interaction study in helicon plasma, to achieve high plasma density and energy absorption efficiency.

On the Core-Shell Nanoparticle in Fractional Dimensional Space

The investigation of core-shell nanoparticles has been greatly exciting in biomedical applications, as this remains of prime importance in targeted drug delivery, sensing, etc. In the present work, the polarizability and scattering features of nanoparticles comprised of nano-sized dielectric/metallic core-shell structures were investigated in the fractional dimensional (FD) space, which essentially relates to the confinement of charged particles. For this purpose, three different kinds of metals—namely aluminum, gold and silver—were considered to form the shell, having a common silicon dioxide (SiO2) nanoparticle as the core. It is noteworthy that the use of noble metal-SiO2 mediums interface remains ideal to realize surface plasmon resonance. The core-shell nanoparticles were considered to have dimensions smaller than the operating wavelength. Under such conditions, the analyses of polarizability and the scattering and absorption cross-sections, and also, the extinction coefficients were taken up under Rayleigh scattering mechanism, emphasizing the effects of a varying FD parameter. Apart from these, the tuning of resonance peaks and the magnitude of surface plasmons due to FD space parameter were also analyzed. It was found that the increase of FD space parameter generally results in blue-shifts in the resonance peaks. Apart from this, the usage of gold and silver shells brings in fairly large shifts in the peak positions of wavelengths, which allows them to be more suitable for a biosensing purpose.

Specific Features of Charged Particle Confinement in the T-15 Tokamak in the Presence of Magnetic Perturbations

Charged particle motion in the regions of magnetic islands and near-separatrix ergodicity of magnetic field lines in the Т-15 tokamak is studied numerically. The trajectories are calculated by integration of exact three-dimensional equations of motion for trapped and passing charged particles starting at different pitch angles. It is shown that the presence of resonant magnetic perturbations qualitatively affects the trajectories of passing particles. In the region of magnetic islands, the orbits of passing particles acquire an island structure, while in the region of the near-separatrix ergodicity of magnetic field lines, the orbits are stochastized. It is shown that magnetic perturbations insignificantly affect trapped particle motion. Even in the absence of magnetic surfaces, the trajectories of trapped particles are regular and their cross sections have the shape of a standard banana orbit. The possibility of charged particles to pass between regions with different magnetic topologies is analyzed.

Simulation of charged particles in Earth's magnetosphere: an approach to the Van Allen belts

Earth's magnetosphere, beyond protecting the ozone layer, is a natural phenomena which allows to study the interaction between charged particles from solar activity and electromagnetic fields. In this paper we studied trajectories of charged particles interacting with a constant dipole magnetic field as first approach of the Earth's magnetosphere using different initial conditions. As a result of this interaction there is a formation of well defined radiation regions by a confinement of charged particles around the lines of the magnetic field. These regions, called Van Allen radiation belts, are described by classical electrodynamics and appear naturally in the numerical modeling done in this work.

Alfvénic gap eigenmode in a linear plasma with ending magnetic throats

To guide the experimental design of a linear plasma device for studying the interaction between energetic ions and Alfvénic gap eigenmode (AGE), this work computes AGE referring to fusion conditions in an ultra-long large plasma cylinder ended with strong magnetic throats for axial confinement of charged particles. It is shown that (i) for uniform equilibrium field between the ending throats, the dispersion relation of the computed wave field agrees well with a simple analytical model for the shear Alfvénic mode and (ii) for periodic equilibrium field with local defect, clear AGE is formed inside the spectral gap for both low and high depths of magnetic throats, although lower depth yields easier observation. The strongest AGE can be on the order of 3.1 × 10−4 to equilibrium field, making it conveniently measurable in experiment. The AGE is a standing wave localized around the defect which is introduced to break the system's periodicity, and its wavelength is twice the system's period, consistent with Bragg's law. The parameter scan reveals that the AGE remains nearly the same when the number of magnetic ripples is reduced from 18 to 8; however, there occurs an upward frequency shift when the depth of magnetic ripples drops from 0.5 to 0.1, possibly due to a flute-like effect: shrinking resonant cavity of the spectral gap.

Threshold speed for two-dimensional confinement of charged particles in certain axisymmetric magnetic fields

In this paper we discuss conditions under which charged particles are confined by an axisymmetric longitudinal magnetic field with power law dependence on the radius. We derive a transcendental equation for the critical speed corresponding to the threshold between bounded and unbounded trajectories of the particles. This threshold speed shows strong dependence on the direction, and this dependence becomes more prominent as the exponent of the power law increases. The equation for threshold speed can be solved exactly for several specific values of the power exponent, but in general it requires a numerical treatment. Remarkably, if the magnetic field magnitude decreases more slowly than the inverse of the radius, charged particles remain confined no matter how large their energies may be.

Plasma Dynamics in a Dual-Frequency Paul Trap Using Tsallis Distribution

This paper theoretically analyzes the motion of a collection of charged particles in a dual-frequency Paul trap. We derive analytical expressions for the single particle trajectory and the plasma distribution function assuming Tsallis statistics to see how this trap configuration is different from a conventional Paul trap. The introduction of a secondary RF frequency in a dual-frequency Paul trap allows for a modification of the spatial extent of confinement of charged particles. The plasma distribution function and temperature have been found to be periodic if the two driving frequencies are rationally related and the resulting period of plasma oscillation is given by the LCM of the time periods corresponding to the two driving frequencies and their linear combinations. The plasma temperature is spatially varying and the time-averaged plasma distribution has been found to be double humped beyond a certain spatial threshold, indicating the presence of certain instabilities. The effect of dual frequency in a Paul trap on the energy level shifts of the atomic orbitals has been investigated and the uncertainties in second order Doppler and Stark shift are found to be of the same order as that of a single-frequency Paul trap.

Study of the stability of charged particle dynamics in a Penning–Malmberg–Surko trap with a rotating field

The solutions of equations characterizing the dynamics of charged particles in electromagnetic Penning–Malmberg traps with a rotating transverse electric field are presented and analyzed. The equations of motion are transformed in a way that makes it possible to distinguish between the motions of magnetron and cyclotron particles, reduce the system of equations to a stationary one, and conclude that asymptotically Lyapunov stable solutions of these equations are lacking in a certain parameter interval. This allows one to optimize the confinement of charged particles in such traps.

Reduced fluid models for self-propelled particles interacting through alignment

The asymptotic analysis of kinetic models describing the behavior of particles interacting through alignment is performed. We will analyze the asymptotic regime corresponding to large alignment frequency where the alignment effects are dominated by the self-propulsion and friction forces. The former hypothesis leads to a macroscopic fluid model due to the fast averaging in velocity, while the second one imposes a fixed speed in the limit, and thus a reduction of the dynamics to a sphere in the velocity space. The analysis relies on averaging techniques successfully used in the magnetic confinement of charged particles. The limiting particle distribution is supported on a sphere, and therefore we are forced to work with measures in velocity. As for the Euler-type equations, the fluid model comes by integrating the kinetic equation against the collision invariants and its generalizations in the velocity space. The main difficulty is their identification for the averaged alignment kernel in our functional setting of measures in velocity.

The effect of particle surface charge density on filter cake properties during dead-end filtration

During the filtration of suspended organic material, filter cakes with high specific resistances are often formed. The properties of these filter cakes differ markedly from the classical filtration properties derived from inorganic suspensions, not only by having a higher specific resistance but also by being highly compressible. These organic substances typically have a high surface charge density, due to the different functional groups on their surfaces, so a set of model particles was synthesized in which the surface charge density can be varied while keeping all other properties constant. The synthesized monodisperse particles all have a polystyrene core and varying ratios of charged (i.e. polyacrylic acid) and uncharged (i.e. hydroxypropyl cellulose) stabilizing polymers covalently grafted to the surface. All used particles have proven to be stable against aggregation during storage and are easily redispersed upon agitation. Aqueous suspensions of the particles were filtered in a dead-end setup at constant pressure to determine the filter cake properties. Results indicate that the specific cake resistance, cake compressibility, and cake porosity increase with the particle surface charge. Comparison with two empirical models of filter cake resistance demonstrates that particle charge is more important than is porosity, as highly charged filter cakes have resistances orders of magnitude higher than calculated, which is not the case for filter cakes of uncharged particles. DLVO theory suggests that the results cannot be explained in terms of classical double-layer effects, even in the extreme case of very small interparticle distances. Deviations from this classical behavior, arising from the confinement of charged particles by charged walls or pores, are a possible explanation, allowing the high resistances to be interpreted as increased osmotic pressure due to the distribution of counterions in the pores. Calculations indicate that osmotic pressure increases with particle charge and with decreasing porosity, but remains close to zero for uncharged particles.

ASYMPTOTIC FIXED-SPEED REDUCED DYNAMICS FOR KINETIC EQUATIONS IN SWARMING

We perform an asymptotic analysis of general particle systems arising in collective behavior in the limit of large self-propulsion and friction forces. These asymptotics impose a fixed speed in the limit, and thus a reduction of the dynamics to a sphere in the velocity variables. The limit models are obtained by averaging with respect to the fast dynamics. We can include all typical effects in the applications: short-range repulsion, long-range attraction, and alignment. For instance, we can rigorously show that the Cucker–Smale model is reduced to a Vicsek-like model without noise in this asymptotic limit. Finally, a formal expansion based on the reduced dynamics allows us to treat the case of diffusion reducing the Cucker–Smale model with diffusion to the non-normalized Vicsek model as in Ref. 29. This technique follows closely the gyroaverage method used when studying the magnetic confinement of charged particles. The main new mathematical difficulty is to deal with measure solutions in this expansion procedure.

Study of a quadrupole ion trap with damping force by the two‐point one block method

The capabilities and performances of a quadrupole ion trap under damping force based on collisional cooling is of particular importance in high-resolution mass spectrometry and should be analyzed by Mathieu's differential solutions. These solutions describe the stability and instability of the ion's trajectories confined in quadrupole devices. One of the methods for solving Mathieu's differential equation is a two-point one block method. In this case, Mathieu's stability diagram, trapping parameters a(z) and q(z) and the secular frequency of the ion motion w(z), can be derived in a precise manner. The two-point one block method (TPOBM) of Adams Moulton type is presented to study these parameters with and without the effect of damping force and compared to the 5th-order Runge-Kutta method (RKM5). The simulated results show that the TPOBM is more accurate and 10 times faster than the RKM5. The physical properties of the confined ions in the r and z axes are illustrated and the fractional mass resolutions m/Δm of the confined ions in the first stability region were analyzed by the RKM5 and the TPOBM. The Lagrange interpolation polynomial was applied in the derivation of the proposed method. The proposed method will be utilized to obtain a series solution directly without reducing it to first order equations. The problem was tested with the ion trajectories in real time with and without the effect of damping force using constant step size. Numerical results from the two-point one block method have been compared with the fifth order Runge-Kutta method. The proposed two-point one block method has a potential application to solve complicated linear and nonlinear equations of the charged particle confinement in a quadrupole field especially in fine tuning accelerators, and, generally speaking, in physics of high energy.

Electric dipole moments: Flavor-diagonal CP violation

Abstract Searches for permanent electric dipole moments of particles, nuclei, atoms and molecules offer an extraordinary discovery potential to new mechanisms of CP violation beyond those incorporated in the standard electroweak model. The electric dipole moments induced by speculative scenarios, on different physical systems, require a complementary approach to pave the way to the fundamental CP-violating mechanisms. New avenues presently being explored in order to improve the experimental sensitivities include projects that consider the trapping of neutral particles, the confinement of charged particles in storage rings as well as the use of radioactive nuclei.

Magnetospheric Vortex Formation: Self-Organized Confinement of Charged Particles

A magnetospheric configuration gives rise to various peculiar plasma phenomena that pose conundrums to astrophysical studies; at the same time, innovative technologies may draw on the rich physics of magnetospheric plasmas. We have created a "laboratory magnetosphere" with a levitating superconducting ring magnet. Here we show that charged particles (electrons) self-organize a stable vortex, in which particles diffuse inward to steepen the density gradient. The rotating electron cloud is sustained for more than 300 s. Because of its simple geometry and self-organization, this system will have wide applications in confining single- and multispecies charged particles.

Nonequatorial charged particle confinement around Kerr black holes

We analyze the nonequatorial charged particle dynamics around a rotating black hole in the presence of an external magnetic field, the latter being given by Wald's exact analytical solution to the Maxwell's equations in the Kerr background. At variance with the corresponding Schwarzschild case, the behavior of the particle becomes here markedly charge-sign dependent, and the more so the more the Kerr parameter increases. The interplay between the rotating black hole and the magnetic field is shown to provide a mechanism both for selective charge ejection in axially collimated jetlike trajectories, and for selective charge confinement into nonequatorial bound orbits around the hole; the possibility of such a confinement allows the fate of an accreting particle to not necessarily be doomed: infall into the hole can be prevented, and the neutrality of the Kerr source could therefore be preserved, while the charge is safely parked into bound cross-equatorial orbits all around it.