scholarly journals Electron Cyclotron collisionless interaction during EC-assisted tokamak start-up

2019 ◽  
Vol 203 ◽  
pp. 01001 ◽  
Author(s):  
Daniela Farina
Keyword(s):  
Energy State ◽  
Particle Interaction ◽  
Beam Width ◽  
Plasma Discharge ◽  
Spatial Profile ◽  
Wave Trapping ◽  
Start Up ◽  
Adiabatic Approach ◽  
Cyclotron Harmonic ◽  
Frequency Harmonic

In the initial phase of a plasma discharge with EC-assisted breakdown, the wave-particle interaction is nonlinear and wave trapping provides the mechanism for transition from a very low energy state to a much larger energy state. A Hamiltonian adiabatic approach provides the condition for the energy variation to occur in a rigorous way, together with quantitative estimate as a function of the wave frequency, harmonic number, polarisation and EC power and beam width, for the first, and second cyclotron harmonic. The interaction is highly localized in space close to the EC resonance. The spatial profile of the energy gain are reported together with the estimates of the width of the radial region where the interaction takes place in the case of a tokamak configuration. The analysis provides a physics based description of the process as well as indications for an optimized experimental setup.

Electron beam-plasma discharge in GDT mirror trap: Experiments on plasma start-up with electron gun

2021 ◽  
Author(s):  
E I Soldatkina ◽  
Egor Pinzhenin ◽  
Olga Korobeynikova ◽  
V V Maximov ◽  
Dmitry Vadimovich Yakovlev ◽  
...  
Keyword(s):  
Electron Beam ◽  
Plasma Discharge ◽  
Initial Energy ◽  
Electron Gun ◽  
Entire Volume ◽  
Neutral Beams ◽  
Beam Plasma ◽  
Start Up ◽  
Gain Energy ◽  
Thin Electron

Abstract The paper describes experiments on the injection of an electron beam into a gas at the Gas Dynamic Trap (GDT) and develops a technique for creating a starting plasma with parameters sufficient for its subsequent heating by neutral beams. It is found that a relatively thin electron beam is capable of ionizing plasma in the entire volume of the trap, and the plasma turbulence it excites is capable of accelerating some of the electrons to energies tens of times higher than the initial energy of the beam. It is shown that, in contrast to early experiments on tabletop open traps, collective beam relaxation under GDT conditions occurs in the vicinity of the entrance magnetic mirror. Since the electron cyclotron frequency in this region significantly exceeds the plasma frequency, it is necessary to study the mechanism of a beam-plasma discharge under these conditions. As a first step along this path, we measure the radial diffusion coefficient of fast particles, as well as the rate at which they gain energy.

Simulation study of energetic-particle driven off-axis fishbone instabilities in tokamak plasmas

2021 ◽  
Author(s):  
Hanzheng Li ◽  
Y Todo ◽  
Hao Wang ◽  
Malik Idouakass ◽  
Jialei Wang
Keyword(s):  
Distribution Function ◽  
Resonance Frequency ◽  
Linear Growth ◽  
Particle Interaction ◽  
Primary Resonance ◽  
Tokamak Plasmas ◽  
Spatial Profile ◽  
Energetic Ions ◽  
Nonlinear Phase ◽  
Drift Frequency

Abstract Kinetic-magnetohydrodynamic hybrid simulations were performed to investigate the linear growth and the nonlinear evolution of off-axis fishbone mode (OFM) destabilized by trapped energetic ions in tokamak plasmas. The spatial profile of OFM is mainly composed of m/n = 2/1 mode inside the q = 2 magnetic flux surface while the m/n = 3/1 mode is predominant outside the q = 2 surface, where m and n are the poloidal and toroidal mode numbers, respectively, and q is the safety factor. The spatial profile of the OFM is a strongly shearing shape on the poloidal plane, suggesting the nonperturbative effect of the interaction with energetic ions. The frequency of the OFM in the linear growth phase is in good agreement with the precession drift frequency of trapped energetic ions, and the frequency chirps down in the nonlinear phase. Two types of resonance conditions between trapped energetic ions and OFM are found. For the first type of resonance, the precession drift frequency matches the OFM frequency, while for the second type, the sum of the precession drift frequency and the bounce frequency matches the OFM frequency. The first type of resonance is the primary resonance for the destabilization of OFM. The resonance frequency which is defined based on precession drift frequency and bounce frequency of the nonlinear orbit for each resonant particle is analyzed to understand the frequency chirping. The resonance frequency of the particles that transfer energy to the OFM chirps down, which may result in the chirping down of the OFM frequency. A detailed analysis of the energetic ion distribution function in phase space shows that the gradient of the distribution function along the E′ = const. line drives or stabilizes the instability, where E′ is a combination of energy and toroidal canonical momentum and conserved during the wave-particle interaction. The distribution function is flattened along the E′ = const. line in the nonlinear phase leading to the saturation of the instability.

scholarly journals The energy of crystal lattices

1930 ◽  
Vol 127 (806) ◽  
pp. 689-703 ◽  
Keyword(s):  
Perturbation Theory ◽  
Energy State ◽  
Wave Functions ◽  
Exclusion Principle ◽  
Original Form ◽  
Spin Moment ◽  
Crystal Lattices ◽  
Initial Wave ◽  
Starting Point ◽  
Adiabatic Approach

In order to calculate the potential energy of a collection of a large number of atoms it is necessary to use the quantum mechanical perturbation theory. The choice of the initial wave functions with which the perturbation calculation is to be carried out, is equivalent to deciding what model of the system shall be taken as the starting point. In the case of crystals the model which involves the simplest assumptions is that in which the crystal is regarded initially as a large number of atoms in their lowest energy state, arranged in a lattice; the lattice constant being great. The perturbation theory is then applied to find how the energy of the system changes as the atoms are brought slowly together; the lattice retaining its original form. It is not necessarily true, however, that when the separation has been reduced to that actually occurring in a given crystal that the system of normal atoms, adiabatically brought together, will be identical with the crystal itself. Thus, for example, Hertzberg has shown that the deepest state of N 2 + does not arise from the adiabatic approach of a normal N atom, and a normal N + ion. When the atoms of the lattice are still well separated it is possible to calculate the mean first order energy using a method given by Heitler. The determinant of the secular equation can be reduced, as Wigner has shown, to a number of irreducible sub-determinants to each of which corresponds a particular term system, and of these, those which satisfy the exclusion principle determine a given total spin moment. The sum of all the energies belonging to one-term system is then given by summing along the diagonal of the corresponding sub-determinant. This procedure, however, assumes that the initial waver functions form an orthogonal set. In the case of a crystal the initial wave functions are to be taken as the product of the wave functions of the separate atoms, and these will only be even approximately orthogonal when the distance between nearest atoms is great.

Start-up phase plasma discharge design of a tokamak via control parameterization method

2015 ◽  
Vol 24 (3) ◽  
pp. 035202 ◽  
Author(s):  
Shan Guo ◽  
Ke Xu ◽  
Chao Xu ◽  
Zhi-Gang Ren ◽  
Bing-Jia Xiao
Keyword(s):  
Plasma Discharge ◽  
Parameterization Method ◽  
Control Parameterization ◽  
Start Up

Resolution in the scanning tunneling microscope

1991 ◽  
Vol 49 ◽  
pp. 488-489
Author(s):  
R. J. Wilson ◽  
D. D. Chambliss ◽  
S. Chiang ◽  
V. M. Hallmark
Keyword(s):  
Scanning Tunneling Microscope ◽  
Fundamental Principle ◽  
Atomic Scale ◽  
Lateral Resolution ◽  
Scanning Tunneling ◽  
Electronic Noise ◽  
Vertical Resolution ◽  
Tunneling Microscopy ◽  
Spatial Profile ◽  
Theoretical Analyses

Scanning tunneling microscopy (STM) has been used for many atomic scale observations of metal and semiconductor surfaces. The fundamental principle of the microscope involves the tunneling of evanescent electrons through a 10Å gap between a sharp tip and a reasonably conductive sample at energies in the eV range. Lateral and vertical resolution are used to define the minimum detectable width and height of observed features. Theoretical analyses first discussed lateral resolution in idealized cases, and recent work includes more general considerations. In all cases it is concluded that lateral resolution in STM depends upon the spatial profile of electronic states of both the sample and tip at energies near the Fermi level. Vertical resolution is typically limited by mechanical and electronic noise.

High-resolution EM study of submicrometer-grained Al-Mg solid solution alloys

1995 ◽  
Vol 53 ◽  
pp. 524-525
Author(s):  
Z. Horita ◽  
D. J. Smith ◽  
M. Furukawa ◽  
M. Nemoto ◽  
R. Z. Valiev ◽  
...  
Keyword(s):  
Electron Microscopy ◽  
Solid Solution ◽  
High Resolution ◽  
Grain Boundaries ◽  
Energy State ◽  
High Energy ◽  
Grain Structure ◽  
Boundary Structure ◽  
Solid Solution Alloy ◽  
Average Grain Size

It is possible to produce metallic materials with submicrometer-grained (SMG) structures by imposing an intense plastic strain under quasi-hydrostatic pressure. Studies using conventional transmission electron microscopy (CTEM) showed that many grain boundaries in the SMG structures appeared diffuse in nature with poorly defined transition zones between individual grains. The implication of the CTEM observations is that the grain boundaries of the SMG structures are in a high energy state, having non-equilibrium character. It is anticipated that high-resolution electron microscopy (HREM) will serve to reveal a precise nature of the grain boundary structure in SMG materials. A recent study on nanocrystalline Ni and Ni3Al showed lattice distortion and dilatations in the vicinity of the grain boundaries. In this study, HREM observations are undertaken to examine the atomic structure of grain boundaries in an SMG Al-based Al-Mg alloy.An Al-3%Mg solid solution alloy was subjected to torsion straining to produce an equiaxed grain structure with an average grain size of ~0.09 μm.

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