scholarly journals Analytic study on low- external ideal infernal modes in tokamaks with large edge pressure gradients

2018 ◽  
Vol 84 (2) ◽  
Author(s):  
Daniele Brunetti ◽  
J. P. Graves ◽  
E. Lazzaro ◽  
A. Mariani ◽  
S. Nowak ◽  
...  
Keyword(s):  
Dispersion Relation ◽  
Safety Factor ◽  
Mass Density ◽  
Analytic Study ◽  
Pressure Gradients ◽  
Plasma Edge ◽  
Vacuum Region ◽  
Metallic Wall ◽  
Equilibrium Profiles ◽  
Pressure Driven

The problem of pressure driven infernal type perturbations near the plasma edge is addressed analytically for a circular limited tokamak configuration which presents an edge flattened safety factor. The plasma is separated from a metallic wall, either ideally conducting or resistive, by a vacuum region. The dispersion relation for such types of instabilities is derived and discussed for two classes of equilibrium profiles for pressure and mass density.

scholarly journals An iterative approach to an arbitrarily short-wavelength solver in global gyrokinetic simulations

2019 ◽  
Vol 85 (1) ◽  
Author(s):  
Alexey Mishchenko ◽  
Roman Hatzky ◽  
Eric Sonnendrücker ◽  
Ralf Kleiber ◽  
Axel Könies
Keyword(s):  
Dispersion Relation ◽  
Short Wavelength ◽  
Linear Case ◽  
Iterative Approach ◽  
Plasma Edge ◽  
Computationally Efficient ◽  
Gyrokinetic Simulations

An iterative formulation of an arbitrarily short-wavelength solver for global gyrokinetic simulations is suggested. The solver is verified against solutions of the dispersion relation. It can be used to treat the nonlinear polarisation density which is important at the plasma edge. In the linear case, the solver is shown to be computationally efficient.

Pressure driven high-n/high-mtearing modes in low shear regions with high pressure gradients and high resistivity

1998 ◽  
Vol 38 (3) ◽  
pp. 325-329 ◽  
Author(s):  
S Günter ◽  
S.D Pinches ◽  
A Gude ◽  
K Hallatschek ◽  
K Lackner ◽  
...  
Keyword(s):  
High Pressure ◽  
High Resistivity ◽  
Pressure Gradients ◽  
Low Shear ◽  
Pressure Driven

scholarly journals The external kink mode in diverted tokamaks

2016 ◽  
Vol 82 (3) ◽  
Author(s):  
A. D. Turnbull ◽  
J. M. Hanson ◽  
F. Turco ◽  
N. M. Ferraro ◽  
M. J. Lanctot ◽  
...  
Keyword(s):  
Safety Factor ◽  
Cross Sections ◽  
Fractional Power ◽  
Plasma Edge ◽  
Flux Surface ◽  
Rational Surfaces ◽  
Kink Mode ◽  
Poloidal Flux ◽  
External Kink ◽  
The Ideal

An explanation is provided for the disruptive instability in diverted tokamaks when the safety factor$q$at the 95 % poloidal flux surface,$q_{95}$, is driven below 2.0. The instability is a resistive kink counterpart to the current-driven ideal mode that traditionally explained the corresponding disruption in limited cross-sections (Shafranov,Sov. Phys. Tech. Phys., vol. 15, 1970, p. 175) when$q_{edge}$, the safety factor at the outermost closed flux surface, lies just below a rational value$m/n$. Experimentally, external kink modes are observed in limiter configurations as the current in a tokamak is ramped up and$q_{edge}$decreases through successive rational surfaces. For$q_{edge}<2$, the instability is always encountered and is highly disruptive. However, diverted plasmas, in which$q_{edge}$is formally infinite in the magnetohydrodynamic (MHD) model, have presented a longstanding difficulty since the theory would predict stability, yet, the disruptive limit occurs in practice when$q_{95}$, reaches 2. It is shown from numerical calculations that a resistive kink mode is linearly destabilized by the rapidly increasing resistivity at the plasma edge when$q_{95}<2$, but$q_{edge}\gg 2$. The resistive kink behaves much like the ideal kink with predominantly kink or interchange parity and no real sign of a tearing component. However, the growth rates scale with a fractional power of the resistivity near the$q=2$surface. The results have a direct bearing on the conventional edge cutoff procedures used in most ideal MHD codes, as well as implications for ITER and for future reactor options.

scholarly journals Classical homogenization to analyse the dispersion relations of spoof plasmons with geometrical and compositional effects

2015 ◽  
Vol 471 (2182) ◽  
pp. 20150472 ◽  
Author(s):  
J.-F. Mercier ◽  
M. L. Cordero ◽  
S. Félix ◽  
A. Ourir ◽  
A. Maurel
Keyword(s):  
Dispersion Relation ◽  
Guided Waves ◽  
Mass Density ◽  
Low Frequency ◽  
Unit Cell ◽  
Real Problem ◽  
Hard Material ◽  
Effective Parameters ◽  
Effective Medium Theories ◽  
Spoof Plasmons

We show that the classical homogenization is able to describe the dispersion relation of spoof plasmons in structured thick interfaces with periodic unit cell being at the subwavelength scale. This is because the interface in the real problem is replaced by a slab of an homogeneous birefringent medium, with an effective mass density tensor and an effective bulk modulus. Thus, explicit dispersion relation can be derived, corresponding to guided waves in the homogenized problem. Contrary to previous effective medium theories or retrieval methods, the homogenization gives effective parameters depending only on the properties of the material and on the geometry of the microstructure. Although resonances in the unit cell cannot be accounted for within this low-frequency homogenization, it is able to account for resonances occurring because of the thickness of the interface and thus, to capture the behaviour of the spoof plasmons. Beyond the case of simple grooves in a hard material, we inspect the influence of tilting the grooves and the influence of the material properties.

Time-Harmonic Waves Propagating Normal to the Layers of Multilayered Periodic Media

1974 ◽  
Vol 41 (1) ◽  
pp. 92-96 ◽  
Author(s):  
Adnan H. Nayfeh
Keyword(s):  
Elastic Modulus ◽  
Dispersion Relation ◽  
Mass Density ◽  
Harmonic Waves ◽  
Periodic Media ◽  
Incident Wavelength ◽  
Time Harmonic ◽  
Periodic Composite ◽  
Special Cases

The dispersion relation is derived for time-harmonic waves propagating normal to the layers of a multilayered periodic composite. The known relations for the homogeneous and the bilaminated media are deduced as special cases. Mixture mass density and elastic modulus are defined in the limit as the ratio of the incident wavelength to the microdimension of the composite approaches infinity.

RELATIONSHIP BETWEEN CURRENT DENSITY AND MASS DENSITY FOR OHMIC TOKAMAK PLASMAS

2008 ◽  
Vol 22 (30) ◽  
pp. 5329-5333 ◽  
Author(s):  
M. ASIF
Keyword(s):  
Safety Factor ◽  
Current Density ◽  
Entire Range ◽  
Mass Density ◽  
Minor Axis ◽  
Tokamak Plasmas ◽  
Magnetic Entropy ◽  
Central Values ◽  
A Value

The relation between current density and mass density in the plasma has been derived based on the assumption that the magnetic entropy is constant in time. Over the entire range of quasi-stationary ohmic conditions, it is obtained [Formula: see text]. Here j0 and ρ0 are the central values of j and ρ with j0 ≈ cB/2πR0 (this corresponds to a value q ≈ 1 of the safety factor near the minor axis).

Mass Determination by Direct Measurement of Electron Scattering

1975 ◽  
Vol 33 ◽  
pp. 240-241
Author(s):  
M. K. Lamvik ◽  
A. V. Crewe
Keyword(s):  
Cross Section ◽  
Electron Scattering ◽  
Mass Density ◽  
Variable Mass ◽  
Scattering Cross Section ◽  
Mass Determination ◽  
Number Density ◽  
Cross Sectional ◽  
Thin Slice ◽  
Scattering Cross

If a molecule or atom of material has molecular weight A, the number density of such units is given by n=Nρ/A, where N is Avogadro's number and ρ is the mass density of the material. The amount of scattering from each unit can be written by assigning an imaginary cross-sectional area σ to each unit. If the current I0 is incident on a thin slice of material of thickness z and the current I remains unscattered, then the scattering cross-section σ is defined by I=IOnσz. For a specimen that is not thin, the definition must be applied to each imaginary thin slice and the result I/I0 =exp(-nσz) is obtained by integrating over the whole thickness. It is useful to separate the variable mass-thickness w=ρz from the other factors to yield I/I0 =exp(-sw), where s=Nσ/A is the scattering cross-section per unit mass.

Image formation analysis of thick biological specimens using three-dimensional power-spectra of through focus series

1994 ◽  
Vol 52 ◽  
pp. 124-125
Author(s):  
Karen F. Han
Keyword(s):  
Inelastic Scattering ◽  
Imaging Techniques ◽  
Mass Density ◽  
Relative Proportion ◽  
Three Dimensional ◽  
Power Spectra ◽  
Image Formation ◽  
Energy Filtering ◽  
Ewald Sphere ◽  
Nonlinear Imaging

The primary focus in our laboratory is the study of higher order chromatin structure using three dimensional electron microscope tomography. Three dimensional tomography involves the deconstruction of an object by combining multiple projection views of the object at different tilt angles, image intensities are not always accurate representations of the projected object mass density, due to the effects of electron-specimen interactions and microscope lens aberrations. Therefore, an understanding of the mechanism of image formation is important for interpreting the images. The image formation for thick biological specimens has been analyzed by using both energy filtering and Ewald sphere constructions. Surprisingly, there is a significant amount of coherent transfer for our thick specimens. The relative amount of coherent transfer is correlated with the relative proportion of elastically scattered electrons using electron energy loss spectoscopy and imaging techniques.Electron-specimen interactions include single and multiple, elastic and inelastic scattering. Multiple and inelastic scattering events give rise to nonlinear imaging effects which complicates the interpretation of collected images.

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