Stochastic Magnetic Field Research Articles

CMB and matter power spectra from cross correlations of primordial curvature and magnetic fields

A complete numerical calculation of the temperature anisotropies and the polarization of the cosmic microwave background is presented for a nonzero cross correlation of a stochastic magnetic field with the primordial curvature perturbation. Such a cross correlation results, for example, if the magnetic field is generated during inflation by coupling electrodynamics to a scalar field that is identified with the curvaton. For a nearly scale-invariant magnetic field of 1 nG it is found that the contribution due to the cross correlation dominates over that of the pure magnetic mode. A similar behavior on large scales is found for the linear matter power spectrum.

3-D effects on viscosity and generation of toroidal and poloidal flows in LHD

Three-dimensional effects on plasma flows have been experimentally studied in the large helical device with 3D configurations. Spontaneous toroidal flow without net driving force using the combination of perpendicular neutral beam injection (NBI) heating and balanced tangential NBI heating has been investigated with two magnetic configurations. Co- and counter-directed spontaneous flows have been observed depending on the collisionality. Toroidal flow shear changes the sign at 0.4<reff<0.6 between co- and counter-flowing plasmas, where reff is a averaged minor radius. The detailed flow structures have been also examined at the edge region with stochastic magnetic field. A poloidal flow driven by the positive radial electric field has been observed at the open field region just outside of the plasma boundary. At the stochastic region, a shear of poloidal flow has been observed, while no shear of toroidal flow has been observed. The toroidal flow shear changes only in the nested magnetic flux surface region. A difference of density fluctuation property has been observed between co- and counter-flowing plasmas, where toroidal flow shears are formed.

Cross correlations from back reaction on stochastic magnetic fields

The induction equation induces non trivial correlations between the primordial curvature mode and the magnetic mode which is a non linear effect.Assuming a stochastic, gaussian magnetic field the resulting power spectra determining the two point cross correlation functions between the primordial curvature perturbation and the magnetic energy density contrast as well as the magnetic anisotropic stressare calculated approximately. The corresponding numerical solutions are used to calculate the angular power spectra determining the temperature anisotropies and polarization of the cosmic microwave background, Cℓ. It is found that the resulting Cℓ are sub-leading in comparison to those generated by the compensated mode for a magnetic field which only redshifts with the expansion of the universe.The main focus are scalar modes, however, vector modes will also be briefly discussed.

Analysis Method for the Low-Order Resistive Interchange Instability in LHD with Stochastic Magnetic Field Line Structure

Analysis Method for the Low-Order Resistive Interchange Instability in LHD with Stochastic Magnetic Field Line Structure

Two-Dimensional Distribution of Electron Temperature in Ergodic Layer of LHD Measured from Line Intensity Ratio of CIV and NeVIII

Two-dimensional distribution of impurity lines emitted from ergodic layer with stochastic magnetic field lines in Large Helical Device (LHD) has been observed using a space-resolved extreme ultraviolet (EUV) spectrometer. The two-dimensional electron temperature distribution in the ergodic layer is successfully measured using the line intensity ratio of Li-like NeVIII 2s-3p ( 2 S1/2- 2 P3/2: 88.09 A, 2 S1/2- 2 P1/2: 88.13 A) to 2p-3s ( 2 P1/22 S1/2: 102.91 A, 2 P3/2- 2 S1/2: 103.09 A) transitions emitted from radial location near Last Closed Flux Surface (LCFS). The intensity ratio analyzed with ADAS code shows no dependence on the electron density below 10 14 cm −3 . The result indicates a little higher temperature, i.e., 220 eV, in the poloidal location at high-field side near helical coils called O-point compared to the temperature near X-point, i.e., 170 eV. The electron temperature profile is also measured at the edge boundary of ergodic layer using the line intensity ratio of Li-like CIV 2p-3d ( 2 P1/2- 2 D3/2: 384.03 A, 2 P3/2- 2 D5/2: 384.18 A) to 2p-3s ( 2 P1/2- 2 S1/2: 419.53 A, 2 P3/2- 2 S1/2: 419.71 A) transitions. The intensity ratios analyzed with CHIANTI, ADAS and T.Kawachi codes show a slightly higher temperature near O-point, i.e., 25 eV for CHIANTI, 21 eV for ADAS and 11 eV for T.Kawachi’s codes, compared to the temperature at X-point, i.e., 15 - 21 eV for CHIANTI, 9 - 15 eV for ADAS and 6 - 9 eV for T.Kawachi codes. It suggests that the transport coefficient in the ergodic layer is varied with three-dimensional structure.

Enhanced heat conductivity in stochastic magnetic field of tokomak affected by the ratio of the parallel to the perpendicular heat diffusivity

Electron heat transport across stochastic magnetic fields is studied numerically in order to find out how the ratio of the parallel to the perpendicular heat diffusivity affects the enhanced heat conductivity and its radial profile in tokomak plasma physics. To find out the details of profile, non-local stochastic magnetic fields, in which the perturbed magnetic islands are separated with each other but very close to in the minor radius of tokomak, are chosen as research objects in our simulation work. Our numerical results indicate that the ratio of the parallel to the perpendicular heat diffusivity is a very important effective factor, which dominate how far the enhanced conductivity contributed by a perturbed magnetic field approach to zero from the rational surface in minor radius. Besides that, a theoretical analysis was provided and compared with the numerical results in this article.

MAGNETIC FIELDS FROM QCD PHASE TRANSITIONS

We study the evolution of QCD phase transition-generated magnetic fields in freely decaying MHD turbulence of the expanding Universe. We consider a magnetic field generation model that starts from basic non-perturbative QCD theory and predicts stochastic magnetic fields with an amplitude of the order of 0.02 $\mu$G and small magnetic helicity. We employ direct numerical simulations to model the MHD turbulence decay and identify two different regimes: "weakly helical" turbulence regime, when magnetic helicity increases during decay, and "fully helical" turbulence, when maximal magnetic helicity is reached and an inverse cascade develops. The results of our analysis show that in the most optimistic scenario the magnetic correlation length in the comoving frame can reach 10 kpc with the amplitude of the effective magnetic field being 0.007 nG. We demonstrate that the considered model of magneto-genesis can provide the seed magnetic field for galaxies and clusters.

Publisher's Note: “Radial profile measurement of electron temperature in edge stochastic magnetic field layer of LHD using intensity ratio of extreme ultraviolet line emissions” [Rev. Sci. Instrum. 83, 10E509 (2012)

Publisher's Note: “Radial profile measurement of electron temperature in edge stochastic magnetic field layer of LHD using intensity ratio of extreme ultraviolet line emissions” [Rev. Sci. Instrum. 83, 10E509 (2012)

Multi-point, high-speed passive ion velocity distribution diagnostic on the Pegasus Toroidal Experiment

A passive ion temperature polychromator has been deployed on Pegasus to study power balance and non-thermal ion distributions that arise during point source helicity injection. Spectra are recorded from a 1 m F/8.6 Czerny-Turner polychromator whose output is recorded by an intensified high-speed camera. The use of high orders allows for a dispersion of 0.02 Å/mm in 4th order and a bandpass of 0.14 Å (~13 km/s) at 3131 Å in 4th order with 100 μm entrance slit. The instrument temperature of the spectrometer is 15 eV. Light from the output of an image intensifier in the spectrometer focal plane is coupled to a high-speed CMOS camera. The system can accommodate up to 20 spatial points recorded at 0.5 ms time resolution. During helicity injection, stochastic magnetic fields keep T(e) low (100 eV) and thus low ionization impurities penetrate to the core. Under these conditions, high core ion temperatures are measured (T(i) ≈ 1.2 keV, T(e) ≈ 0.1 keV) using spectral lines from carbon III, nitrogen III, and boron IV.

Radial profile measurement of electron temperature in edge stochastic magnetic field layer of LHD using intensity ratio of extreme ultraviolet line emissions

Vertical profile of neon line emissions in 30-650 Å wavelength range has been observed in horizontally elongated plasma cross section of Large Helical Device (LHD). Intensity ratio between the neon line emissions is studied to measure the radial profile of electron temperature in the edge stochastic magnetic field layer of LHD. The edge temperature profile successfully obtained from the line ratio of NeVIII 2s-3p to 2p-3s transitions is compared with the simulation based on three-dimensional edge transport code. The result shows a reasonably good agreement with the edge temperature profile analyzed from atomic data and analysis structure code. The electron temperature at last closed flux surface measured from the intensity ratio is also in good agreement with that measured from Thomson scattering.

Study on Electron Heat Diffusion Across Stochastic Magnetic Field Affected by Magnitude of Perturbed Magnetic Field in Tokomak

Electron heat diffusion across stochastic magnetic fields is studied numerically in order to find out how the magnitude of perturbed magnetic field affect the enhanced heat conductivity and its radial profile in tokomak plasma physics. For these purposes, non-local stochastic magnetic fields are chosen as research objects in our simulation work. From our numerical results, we can find that the effects of the perturbed magnetic field magnitude are dominated parameter on the enhance electron heat transport conductivity wherever the magnetic field is single island or full stochastic field. Also, a theoretical analysis is provided and compared with numerical results.

Analysis of stochastic magnetic fields formed by the application of resonant magnetic perturbations on MAST and comparison with experiment

In MAST experiments with applied resonant magnetic perturbations (RMPs), clear reduction in line-averaged density has been observed in a wide range of L-mode plasmas when there is an alignment between the perturbation and the equilibrium magnetic field that maximizes the size of the resonant components of the applied magnetic field, as well as in a few H-mode plasmas but with a much stronger sensitivity to this alignment. This density pump-out is the result of increased particle transport, which is thought to be caused by the formation of a stochastic magnetic field in the plasma edge. This paper presents an analysis of the magnetic field structures formed by the application of n = 3 RMPs on MAST, including various parameters characterizing the degree of stochasticity in the plasma edge. Values for these parameters are calculated and compared with the amount of density pump-out observed in MAST experiments. It is found that density pump-out is fairly well correlated with some of the parameters calculated using vacuum modelling, but none of them provides a single threshold value for pump-out that applies to both L- and H-mode plasmas. Plasma response modelling provides a robust criterion for density pump-out that applies both to L- and H-mode plasmas.

Screening of resonant magnetic perturbations taking into account a self-consistent electric field

Steady-state screening of resonant magnetic perturbations (RMPs) in a tokamak is analysed taking into account a self-consistent electric field. On the one hand, the self-consistent radial electric field is determined by the balance of the electron radial conductivity in a stochastic magnetic field screened by the plasma and by the neoclassical ion conductivity. On the other hand, the parallel current of electrons, the radial projection of which is balanced by the ion current, determines the screening of RMPs. In this work, the self-consistent electric field and RMP screening are calculated. Two different regimes of screening are found: the ‘ion’ branch which corresponds to the negative radial electric field and the ‘electron’ branch for which the electric field is positive. Predictions of the model are compared with the experimental data and results of the simulation with various codes. The corresponding toroidal rotation and pump-out effect are discussed.

Effects of helical magnetic fields on the cosmic microwave background

A complete numerical calculation of the temperature anisotropies and polarization of the cosmic microwave background in the presence of a stochastic helical magnetic field is presented which includes the contributions due to scalar, vector and tensor modes. The correlation functions of the magnetic field contributions are calculated numerically including a Gaussian window function to effectively cut off the magnetic field spectrum due to damping. Apart from parity-even correlations the helical nature of the magnetic field induces parity-odd correlations between the $E$ and $B$ mode of polarization as well as between temperature ($T$) and the polarization $B$ mode.

Two-dimensional measurement of edge impurity emissions using space-resolved extreme ultraviolet spectrometer in Large Helical Device

A space-resolved extreme ultraviolet (EUV) spectrometer working in wavelength range of 50-500 Å has been developed to measure two-dimensional distribution of impurity spectral lines emitted from edge plasma of Large Helical Device (LHD), in which the magnetic field is formed by stochastic magnetic field with three-dimensional structure called ergodic layer. The two-dimensional measurement of edge impurity line emissions is carried out by scanning horizontally the observation chord of the space-resolved EUV spectrometer during single LHD discharge. Images of CIV (312.4 Å) and HeII (303.78 Å) are presented as the first result. The results are compared with ones calculated from the edge chord length in the ergodic layer of LHD plasma.

Plasma Edge Transport with Stochastic Magnetic Field Structures

Controlling the transport in the plasma edge of high temperature plasmas has recently been extended by a sophisticated option - the stochastization of the magnetic cage confining the plasma. The idea is to induce a chaotic magnetic field structure in the edge which can act as a magnetic valve to control heat and particle fluxes between the confined plasma and the plasma facing components. This tool is applied in both, stellarators as well as tokamaks. In this lecture an introduction into the topic will be given. The topics are (a) generation and structure of chaotic magnetic edge layers, (b) plasma transport with stochastic magnetic fields including the resulting three-dimensional plasma wall interaction and (c) impact of a plasma response. However, this field is matter of intense ongoing research and hence this lecture gives a systematic introduction into the challenges based on examples from the TEXTOR tokamak.

Measurement of heavy-hole spin dephasing in (InGa)As quantum dots

We measure the spin dephasing of holes localized in self-assembled (InGa)As quantum dots by spin noise spectroscopy. The localized holes show a distinct hyperfine interaction with the nuclear spin bath despite the p-type symmetry of the valence band states. The experiments reveal a short spin relaxation time {\tau}_{fast}^{hh} of 27 ns and a second, long spin relaxation time {\tau}_{slow}^{hh} which exceeds the latter by more than one order of magnitude. The two times are attributed to heavy hole spins aligned perpendicular and parallel to the stochastic nuclear magnetic field. Intensity dependent measurements and numerical simulations reveal that the long relaxation time is still obscured by light absorption, despite low laser intensity and large detuning. Off-resonant light absorption causes a suppression of the spin noise signal due to the creation of a second hole entailing a vanishing hole spin polarization.

Twinkling pulsar wind nebulae in the synchrotron cut-off regime and the γ-ray flares in the Crab Nebula

ABSTRACT Synchrotron radiation of ultrarelativistic particles accelerated in a pulsar wind nebula may dominate its spectrum up to γ-ray energies. Because of the short cooling time of the γ-ray-emitting electrons and positrons, the γ-ray-emission zone is in the immediate vicinity of the acceleration site. Particle acceleration likely occurs at the termination shock of a relativistic striped wind, where multiple forced magnetic field reconnections provide strong magnetic fluctuations facilitating Fermi acceleration processes. The acceleration mechanisms imply the presence of stochastic magnetic fields in the particle acceleration region, which cause stochastic variability of the synchrotron emission. This variability is particularly strong in the steep γ-ray tail of the spectrum, where modest fluctuations of the magnetic field lead to strong flares of spectral flux. In particular, stochastic variations of magnetic field, which may lead to quasi-cyclic γ-ray flares, can be produced by the relativistic cyclotron ion instability at the termination shock. Our model calculations of the spectral and temporal evolution of synchrotron emission in the spectral cut-off regime demonstrate that the intermittent magnetic field concentrations dominate the γ-ray emission from highest energy electrons and provide fast, strong variability even for a quasi-steady distribution of radiating particles. The simulated light curves and spectra can explain the very strong γ-ray flares observed in the Crab Nebula and lack of strong variations at other wavelengths. The model predicts high polarization in the flare phase, which can be tested with future polarimetry observations.

Evidence for a resonant cyclotron interaction between runaway electrons and MHD modes in the experimental advanced superconducting tokamak

In the past, the resonant cyclotron interaction between runaway electrons and lower hybrid waves via anomalous Doppler broadening was experimentally investigated, and it was shown to be able to create a barrier to the energy that could be reached by the runaway electrons [E. Li et al., Nucl. Instrum. Methods Phys. Res. A 621, 566 (2010)]. In this paper, to our knowledge for the first time, experimental evidence will be provided for a resonant cyclotron interaction between runaway electrons and magnetohydrodynamics modes in a stochastic magnetic field in the experimental advanced superconducting tokamak (EAST), which has been theoretically proposed as a mechanism able to limit the maximum attainable energy by runaway electrons in tokamak plasmas [J. R. Martín-Solís and R. Sánchez, Phys. Plasmas 15, 112505 (2008)].

Overview of results from the Large Helical Device

The physical understanding of net-current-free helical plasmas has progressed in the Large Helical Device (LHD) since the last Fusion Energy Conference in Geneva, 2008. The experimental results from LHD have promoted detailed physical documentation of features specific to net-current-free 3D helical plasmas as well as complementary to the tokamak approach. The primary heating source is neutral beam injection (NBI) with a heating power of 23 MW, and electron cyclotron heating with 3.7 MW plays an important role in local heating and power modulation in transport studies. The maximum central density has reached 1.2 × 1021 m−3 due to the formation of an internal diffusion barrier (IDB) at a magnetic field of 2.5 T. The IDB is maintained for 3 s by refuelling with repetitive pellet injection. In a different operational regime with moderate density less than 2 × 1019 m−3, a plasma with a central ion temperature reaching 5.6 keV exhibits the formation of an internal transport barrier (ITB). The ion thermal diffusivity decreases to the level predicted by neoclassical transport. In addition to the rotation driven by the momentum input due to tangential NBI, the existence of intrinsic torque to drive toroidal rotation is identified in the plasma with an ITB. This ITB is accompanied by an impurity hole which generates an impurity-free core. The impurity hole is due to a large outward convection of impurities in spite of the negative radial electric field. The magnitude of the impurity hole is enhanced in the magnetic configuration with a large helical ripple and for heavier atoms. Another mechanism for suppressing impurity contamination is identified at the plasma edge with a stochastic magnetic field. A helical system shares common physics issues with tokamaks such as 3D equilibria, transport in a stochastic magnetic field, plasma response to a resonant magnetic perturbation, divertor physics and the role of radial electric field and meso-scale structure.