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Title: Spectral Analysis of Non-ideal MRI Modes: The Effect of Hall Diffusion

Abstract

The effect of magnetic field diffusion on the stability of accretion disks is a problem that has attracted considerable interest of late. In particular, the Hall effect has the potential to bring about remarkable changes in the dynamical behavior of disks that are without parallel. In this paper, we conduct a systematic examination of the linear eigenmodes in a weakly magnetized differentially rotating gas with a special focus on Hall diffusion. We first develop a geometrical representation of the eigenmodes and provide a detailed quantitative description of the polarization properties of the oscillatory modes under the combined influence of the Coriolis and Hall effects. We also analyze the effects of magnetic diffusion on the structure of the unstable modes and derive analytical expressions for the kinetic and magnetic stresses and energy densities associated with the non-ideal magnetorotational instability (MRI). Our analysis explicitly demonstrates that, if the dissipative effects are relatively weak, the kinetic stresses and energies make up the dominant contribution to the total stress and energy density when the equilibrium angular momentum and magnetic field vectors are anti-parallel. This is in sharp contrast to what is observed in the case of the ideal or dissipative MRI. We conduct shearingmore » box simulations and find very good agreement with the results derived from linear theory. Because the modes under consideration are also exact solutions of the nonlinear equations, the unconventional nature of the kinetic and magnetic stresses may have significant implications for the nonlinear evolution in some regions of protoplanetary disks.« less

Authors:
;  [1]
  1. Niels Bohr International Academy, Niels Bohr Institute, Blegdamsvej 17, DK-2100, Copenhagen Ø (Denmark)
Publication Date:
OSTI Identifier:
22661250
Resource Type:
Journal Article
Resource Relation:
Journal Name: Astrophysical Journal; Journal Volume: 838; Journal Issue: 1; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ACCRETION DISKS; ANGULAR MOMENTUM; DIFFUSION; ENERGY DENSITY; EQUATIONS; EQUILIBRIUM; EVOLUTION; EXACT SOLUTIONS; HALL EFFECT; INSTABILITY; MAGNETIC FIELDS; MAGNETOHYDRODYNAMICS; NMR IMAGING; POLARIZATION; PROTOPLANETS; SIMULATION; STABILITY; STRESSES

Citation Formats

Mohandas, Gopakumar, and Pessah, Martin E., E-mail: gopakumar@nbi.ku.dk, E-mail: mpessah@nbi.ku.dk. Spectral Analysis of Non-ideal MRI Modes: The Effect of Hall Diffusion. United States: N. p., 2017. Web. doi:10.3847/1538-4357/AA6118.
Mohandas, Gopakumar, & Pessah, Martin E., E-mail: gopakumar@nbi.ku.dk, E-mail: mpessah@nbi.ku.dk. Spectral Analysis of Non-ideal MRI Modes: The Effect of Hall Diffusion. United States. doi:10.3847/1538-4357/AA6118.
Mohandas, Gopakumar, and Pessah, Martin E., E-mail: gopakumar@nbi.ku.dk, E-mail: mpessah@nbi.ku.dk. Mon . "Spectral Analysis of Non-ideal MRI Modes: The Effect of Hall Diffusion". United States. doi:10.3847/1538-4357/AA6118.
@article{osti_22661250,
title = {Spectral Analysis of Non-ideal MRI Modes: The Effect of Hall Diffusion},
author = {Mohandas, Gopakumar and Pessah, Martin E., E-mail: gopakumar@nbi.ku.dk, E-mail: mpessah@nbi.ku.dk},
abstractNote = {The effect of magnetic field diffusion on the stability of accretion disks is a problem that has attracted considerable interest of late. In particular, the Hall effect has the potential to bring about remarkable changes in the dynamical behavior of disks that are without parallel. In this paper, we conduct a systematic examination of the linear eigenmodes in a weakly magnetized differentially rotating gas with a special focus on Hall diffusion. We first develop a geometrical representation of the eigenmodes and provide a detailed quantitative description of the polarization properties of the oscillatory modes under the combined influence of the Coriolis and Hall effects. We also analyze the effects of magnetic diffusion on the structure of the unstable modes and derive analytical expressions for the kinetic and magnetic stresses and energy densities associated with the non-ideal magnetorotational instability (MRI). Our analysis explicitly demonstrates that, if the dissipative effects are relatively weak, the kinetic stresses and energies make up the dominant contribution to the total stress and energy density when the equilibrium angular momentum and magnetic field vectors are anti-parallel. This is in sharp contrast to what is observed in the case of the ideal or dissipative MRI. We conduct shearing box simulations and find very good agreement with the results derived from linear theory. Because the modes under consideration are also exact solutions of the nonlinear equations, the unconventional nature of the kinetic and magnetic stresses may have significant implications for the nonlinear evolution in some regions of protoplanetary disks.},
doi = {10.3847/1538-4357/AA6118},
journal = {Astrophysical Journal},
number = 1,
volume = 838,
place = {United States},
year = {Mon Mar 20 00:00:00 EDT 2017},
month = {Mon Mar 20 00:00:00 EDT 2017}
}
  • Hall-effect thruster plasma oscillations recorded by means of probes located at the channel exit are analyzed using the empirical mode decomposition (EMD) method. This self-adaptive technique permits to decompose a nonstationary signal into a set of intrinsic modes, and acts as a very efficient filter allowing to separate contributions of different underlying physical mechanisms. Applying the Hilbert transform to the whole set of modes allows to identify peculiar events and to assign them a range of instantaneous frequency and power. In addition to 25 kHz breathing-type oscillations which are unambiguously identified, the EMD approach confirms the existence of oscillations withmore » instantaneous frequencies in the range of 100-500 kHz typical for ion transit-time oscillations. Modeling of high-frequency modes ({nu}{approx}10 MHz) resulting from EMD of measured wave forms supports the idea that high-frequency plasma oscillations originate from electron-density perturbations propagating azimuthally with the electron drift velocity.« less
  • The nonlinear dynamics of ideal, incompressible Hall magnetohydrodynamics (HMHD) is investigated through classical Gibbs ensemble methods applied to the finite Galerkin representation. The spectral structure of HMHD is derived in a three-dimensional periodic geometry and compared with the MHD case. This provides a general picture of spectral transfer and cascade by the assumption that ideal Galerkin HMHD follows equilibrium statistics as in the case of Euler [U. Frisch et al., J. Fluid Mech. 68, 769 (1975)] and MHD [T. Stribling and W. H. Matthaeus, Phys. Fluids B 2, 1979 (1990)] theories. In HMHD, the equilibrium ensemble is built on themore » conservation of three quadratic invariants: The total energy, the magnetic helicity, and the generalized helicity. The latter replaces the cross helicity in MHD. In HMHD equilibrium, several differences appear with respect to the MHD case: (i) The generalized helicity (and in a weaker way the energy and the magnetic helicity) tends to condense in the longest wavelength, as in MHD, but also admits the novel feature of spectral enhancement, not a true condensation, at the smallest scales; (ii) equipartition between kinetic and magnetic energy, typical of Alfvenic MHD turbulence, is broken; (iii) modal distributions of energy and helicities show minima due to the presence of the ion skin depth. Ensemble predictions are compared to numerical simulations with a low-order truncation Galerkin spectral code, and good agreement is seen. Implications for general turbulent states are discussed.« less
  • Purpose: To report our initial experience of systematic monitoring treatment response using longitudinal diffusion MR images on a Co-60 MRI-guided radiotherapy system. Methods: Four patients, including 2 head-and-necks, 1 sarcoma and 1 GBM treated on a 0.35 Tesla MRI-guided treatment system, were analyzed. For each patient, 3D TrueFISP MRIs were acquired during CT simulation and before each treatment for treatment planning and patient setup purposes respectively. Additionally, 2D diffusion-weighted MR images (DWI) were acquired weekly throughout the treatment course. The gross target volume (GTV) and brainstem (as a reference structure) were delineated on weekly 3D TrueFISP MRIs to monitor anatomymore » changes, the contours were then transferred onto the corresponding DWI images after fusing with the weekly TrueFISP images. The patient-specific temporal and spatial variations during the entire treatment course, such as anatomic changes, target apparent diffusion coefficient (ADC) distribution were evaluated in a longitudinal pattern. Results: Routine MRI revealed progressive soft-tissue GTV volume changes (up to 53%) for the H&N cases during the treatment course of 5–7 weeks. Within the GTV, the mean ADC values varied from −44% (ADC decrease) to +26% (ADC increase) in a week. The gradual increase of ADC value was inversely associated with target volume variation for one H&N case. The maximal changes of mean ADC values within the brainstem were 5.3% for the H&N cases. For the large size sarcoma and GBM tumors, spatial heterogeneity and temporal variations were observed through longitudinal ADC analysis. Conclusion: In addition to the superior soft-tissue visualization, the 0.35T MR system on ViewRay showed the potential to quantitatively measure the ADC values for both tumor and normal tissues. For normal tissue that is minimally affected by radiation, its ADC values are reproducible. Tumor ADC values show temporal and spatial fluctuation that can be exploited for personalized adaptive therapy.« less
  • The TERPSICHORE three-dimensional linear ideal magnetohydrodynamic (MHD) stability code ({ital Theory} {ital of} {ital Fusion} {ital Plasmas}, Proceedings of the Joint Varenna--Lausanne International Workshop, Chexbres, Switzerland, 1988 (Editrice Compositori, Bologna, Italy, 1989), p. 93; {ital Controlled} {ital Fusion} {ital and} {ital Plasma} {ital Heating}, Proceedings of the 17th European Conference, Amsterdam, The Netherlands (European Physical Society, Petit-Lancy, Switzerland, 1990), Vol. 14B, Part II, p. 931; {ital Theory} {ital of} {ital Fusion} {ital Plasmas}, Proceedings of the Joint Varenna--Lausanne International Workshop, Valla Monastero, Varenna, Italy, 1990 (Editrice Compositori, Bologna, Italy, 1990), p. 655) has been extended to the full MHD equations.more » The new code is used to calculate the physical growth rates of nonlocal low-{ital n} modes for {ital l}=2 torsatron configurations. A comprehensive investigation of the relation between the Mercier modes and the low-{ital n} modes has been performed. The unstable localized low-{ital n} modes are found to be correlated with the Mercier criterion. Finite growth rates of the low-{ital n} modes correspond to finite values of the Mercier criterion parameter. Near the Mercier marginal stability boundary, the low-{ital n} modes tend to be weakly unstable with very small growth rates. However, the stability of global-type low-{ital n} modes is found to be decorrelated from that of Mercier modes. The low-{ital n} modes with global radial structures can be more stable or more unstable than Mercier modes.« less
  • Purpose: Diffusion-weighted imaging(DWI) has been shown to have superior tumor-to-tissue contrast for cancer detection.This study aims at developing and evaluating a four dimensional DWI(4D-DWI) technique using retrospective sorting method for imaging respiratory motion for radiotherapy planning,and evaluate its effect on Apparent Diffusion Coefficient(ADC) measurement. Materials/Methods: Image acquisition was performed by repeatedly imaging a volume of interest using a multi-slice single-shot 2D-DWI sequence in the axial planes and cine MRI(served as reference) using FIESTA sequence.Each 2D-DWI image were acquired in xyz-diffusion-directions with a high b-value(b=500s/mm2).The respiratory motion was simultaneously recorded using bellows.Retrospective sorting was applied in each direction to reconstruct 4D-DWI.Themore » technique was evaluated using a computer simulated 4D-digital human phantom(XCAT),a motion phantom and a healthy volunteer under an IRB-approved study.Motion trajectories of regions-of-interests(ROI) were extracted from 4D-DWI and compared with reference.The mean motion trajectory amplitude differences(D) between the two was calculated.To quantitatively analyze the motion artifacts,XCAT were controlled to simulate regular motion and the motions of 10 liver cancer patients.4D-DWI,free-breathing DWI(FB- DWI) were reconstructed.Tumor volume difference(VD) of each phase of 4D-DWI and FB-DWI from the input static tumor were calculated.Furthermore, ADC was measured for each phase of 4D-DWI and FB-DWI data,and mean tumor ADC values(M-ADC) were calculated.Mean M-ADC over all 4D-DWI phases was compared with M-ADC calculated from FB-DWI. Results: 4D-DWI of XCAT,the motion phantom and the healthy volunteer demonstrated the respiratory motion clearly.ROI D values were 1.9mm,1.7mm and 2.0mm,respectively.For motion artifacts analysis,XCAT 4D-DWI images show much less motion artifacts compare to FB-DWI.Mean VD for 4D-WDI and FB-DWI were 8.5±1.4% and 108±15%,respectively.Mean M-ADC for ADC measured from 4D-DWI and M-ADC measured from FB-DWI were (2.29±0.04)*0.001*mm2/s and (3.80±0.01)*0.001*mm2/s,respectively.ADC value ground-truth is 2.24*0.001*mm2/s from the input of the simulation. Conclusion: A respiratory correlated 4D-DWI technique has been initially evaluated in phantoms and a human subject.Comparing to free breathing DWI,4D-DWI can lead to more accurate measurement of ADC.« less