Magnetic reconnection triggering magnetohydrodynamic instabilities during a sawtooth crash in a Tokamak plasma

Thomson scattering measurements with subcentimeter spatial resolution have been made during a sawtooth crash in a Mega Ampere Spherical Tokamak fusion plasma. The unparalleled resolution of the temperature profile has shed new light on the mechanisms that underlie the sawtooth. As magnetic reconnection occurs, the temperature gradient at the island boundary increases. The increased local temperature gradient is sufficient to make the helical core unstable to ideal magnetohydrodynamic instabilities, thought to be responsible for the rapidity of the collapse.     

Generation of suprathermal electrons during magnetic reconnection at the sawtooth crash and disruption instability in the T-10 tokamak

Evidence for excitation of suprathermal electrons ( E(gamma) approximately 20-100 keV) during magnetic reconnection in the T-10 tokamak is presented through analysis of the x-ray measurements with enhanced spatial and time resolution. A toroidally viewing x-ray imaging system and a fast hard x-ray detector placed inside the tokamak vessel allow identification of bursts of the nonthermal x-ray radiation around X points of the m = 1 and m = 2 magnetic islands during the sawtooth crash and prior to the energy quench at the density limit disruption.     

Cantori spectra for the sawtooth map

Summary We calculate analytically the Fourier spectrum for the cantori of the sawtooth maps. These maps are a one-parameter family of chaotic area-preserving maps. We show that the Fourier spectrum grows exponentially for parameters close to criticality, and that it exhibits self-similarity structure at all length scales. The self-similarity scales as the quotients of successive denominators of the convergents of irrational numbers. We compute exactly the scaling for quadratic irrationals. The behaviour of the spectrum for large values of the perturbation parameter is also investigated. The author of this paper has agreed to not receive the proofs for correction.     

Rigorous diffusion properties for the sawtooth map

We get a rigorous bound for the diffusion constant of the hamiltonian dynamical system generated by a sawtooth map on a cylinder. The momentum variable properly renormalized then behaves almost like a brownian motion in the limit of infinite coupling constants. The strategy of the proof is a rigorous reformulation of the Random Phase Approximation.Supported by Contract CEE n⁰ SC1^*0281     

Magnetic reconnection in collisionless plasmas

A class of processes involving magnetic field reconnection, in collisionless plasmas and magnetic configurations where the field undergoes a finite change of direction, is investigated. Reconnecting modes that rely on the effects of electron Landau resonance and density gradient for their excitation are found to require the analytical or numerical treatment of four consecutive asymptotic regions. The influence of finite electron temperature gradient in the region where the effects of electron Landau resonance prevail, and the convection of energy toward the region where ion Landau resonance is dominant tend to dampen these modes. Conversely, significant distortions of the ion distribution can follow their excitation. The relevance of the obtained results to experimental observations on laboratory plasmas and in space physics is discussed. Different processes are involved with magnetic reconnection in magnetic configurations where the field does not have appreciable shear but has a neutral surface on which it vanishes.     

Exact energy principle in magnetic reconnection for current-sheet models

On the basis of an exact nonlinear energy principle, it is shown that the change in magnetic topology (i.e., reconnection) in a finite-domain system leads to the conversion of magnetic field energy to particle energy. However, it is also shown that the conversion efficiency gradually disappears as the system size increases. This principle is demonstrated with model current-sheet equilibria including Harris and Fadeev solutions, as well as a current-sheet equilibrium which contains a singular current layer. The finding that energy conversion in reconnection is highly dependent on the system size may have an important implication for numerical simulations performed under finite geometry.     

A linear code for the sawtooth and cat maps

The sawtooth maps are a one-parameter set of piecewise linear area preserving maps on the torus. For positive integer values of the parameter K they are automorphisms of the torus, known as the cat maps. We present a symbolic dynamics for these maps in which the symbols are integers. This code is related to a practical problem of the stabilisation of a system which is perturbed by impulses. The code is linear in the sense that an orbit and its code are linearly related, so it is not difficult to obtain a good approximation to one from the other in practice. A stationary stochastic process for generating the code is given explicitly. The theory uses Green function methods, which are also used to study ordered periodic orbits and cantori. The problems of using a similar code for arbitrary area preserving twist maps on the torus are briefly discussed.     

Catastrophe model for fast magnetic reconnection onset

A catastrophe model for the onset of fast magnetic reconnection is presented that suggests why plasma systems with magnetic free energy remain apparently stable for long times and then suddenly release their energy. For a given set of plasma parameters there are generally two stable reconnection solutions: a slow (Sweet-Parker) solution and a fast (Alfvénic) Hall reconnection solution. Below a critical resistivity the slow solution disappears and fast reconnection dominates. Scaling arguments predicting the two solutions and the critical resistivity are confirmed with two-fluid simulations.     

不可压缩等离子体的2维磁场重联模型

提出了一种2维磁场重联模型。磁场重联过程中的电荷分离在等离子体中产生静电场,等离子体在电场中的漂移运动可以解释阿尔芬速度量级的出流。该磁场重联模型给出如下结论：Sweet-Parker模型描述的重联率强烈地依赖于电子质量与离子质量之比;反常电阻率正比于离子惯性长度和电流片宽度比值的平方; 相对论效应和高温等离子体中电子-正电子对的产生可以提高重联率; 电磁波的激发对于磁能的损耗是必要的。     

Elliptic behaviour in the sawtooth standard map

This paper examines the standard map with sawtooth nonlinearity when the eigenvalues of the Jacobian lie on the unit circle. This is an area-preserving map of the torus to itself that is linear except on a line on which it is discontinuous. We discuss the closure of the set of images of the discontinuity and present numerical evidence that its Lebesgue measure is positive. Moreover, we present evidence that the measure of the closure of images of the discontinuity changes continuously with the parameter k. This means that the sawtooth standard map may exhibit coexistence of two positive measure subsets on which the dynamics is respectively regular and irregular in a certain sense. In the appendix we show that this map is equivalent to a map studied by electronics engineers as a model for the quiescent behaviour of a linear lossless digital filter with “two's complement” overflow.     

不可压缩等离子体的2维磁场重联模型

提出了一种2维磁场重联模型。磁场重联过程中的电荷分离在等离子体中产生静电场,等离子体在电场中的漂移运动可以解释阿尔芬速度量级的出流。该磁场重联模型给出如下结论:Sweet-Parker模型描述的重联率强烈地依赖于电子质量与离子质量之比;反常电阻率正比于离子惯性长度和电流片宽度比值的平方; 相对论效应和高温等离子体中电子-正电子对的产生可以提高重联率; 电磁波的激发对于磁能的损耗是必要的。     

Z箍缩等离子体磁重联现象

分析了磁重联对晕等离子体加速和能量平衡过程的影响。分析表明晕等离子体向轴心的加速过程分为两个阶段:第一阶段晕等离子体在磁压或热压(依赖于丝数)作用下向轴心运动;第二阶段晕等离子体由于磁重联过程被加速到阿尔芬速度,并到达轴心形成先驱等离子体。估算表明重联层的厚度与离子的惯性长度具有相同的数量级,电流片内电子运动和离子的运动是解耦合的。在内爆滞止阶段电荷分离产生强的径向电场,这个电场将磁能转化为等离子体轴向(z方向)动能,内爆动能和轴向动能共同转化为X射线辐射能,以此解释了X射线能量大于内爆动能这一观测结果。分析了磁重联电磁脉冲的性质,对于1 MA驱动条件,电磁脉冲的总能量可达kJ量级。     

Z箍缩等离子体磁重联现象

分析了磁重联对晕等离子体加速和能量平衡过程的影响。分析表明晕等离子体向轴心的加速过程分为两个阶段:第一阶段晕等离子体在磁压或热压(依赖于丝数)作用下向轴心运动;第二阶段晕等离子体由于磁重联过程被加速到阿尔芬速度,并到达轴心形成先驱等离子体。估算表明重联层的厚度与离子的惯性长度具有相同的数量级,电流片内电子运动和离子的运动是解耦合的。在内爆滞止阶段电荷分离产生强的径向电场,这个电场将磁能转化为等离子体轴向(z方向)动能,内爆动能和轴向动能共同转化为X射线辐射能,以此解释了X射线能量大于内爆动能这一观测结果。分析了磁重联电磁脉冲的性质,对于1 MA驱动条件,电磁脉冲的总能量可达kJ量级。     

Bayesian log-periodic model for financial crashes

This paper introduces a Bayesian approach in econophysics literature about financial bubbles in order to estimate the most probable time for a financial crash to occur. To this end, we propose using noninformative prior distributions to obtain posterior distributions. Since these distributions cannot be performed analytically, we develop a Markov Chain Monte Carlo algorithm to draw from posterior distributions. We consider three Bayesian models that involve normal and Student’s t-distributions in the disturbances and an AR(1)-GARCH(1,1) structure only within the first case. In the empirical part of the study, we analyze a well-known example of financial bubble – the S&P 500 1987 crash – to show the usefulness of the three methods under consideration and crashes of Merval-94, Bovespa-97, IPCMX-94, Hang Seng-97 using the simplest method. The novelty of this research is that the Bayesian models provide 95% credible intervals for the estimated crash time.     

Ion acceleration during reconnection in MAST

Spontaneous acceleration of ions to suprathermal energies is observed during magnetic reconnection in the Mega-Ampere Spherical Tokamak (MAST). A high-energy tail is observed in the ion-distribution function following each internal reconnection event in Ohmic discharges. This phenomenon is explained in terms of runaway ion acceleration in the electric field induced by the reconnection.     

Collisionless reconnection in an electron-positron plasma

Electromagnetic particle-in-cell simulations of fast collisionless reconnection in a two-dimensional electron-positron plasma (without an equilibrium guide field) are presented. A generalized Ohm's law in which the Hall current cancels out exactly is given. It is suggested that the key to fast reconnection in this plasma is the localization caused by the off-diagonal components of the pressure tensors, which produce an effect analogous to a spatially localized resistivity.