Fast growing double tearing modes in a tokamak plasma

Configurations with nearby multiple resonant surfaces have broad spectra of linearly unstable coupled tearing modes with dominant high poloidal mode numbers m. This was recently shown for the case of multiple q = 1 resonances [Bierwage et al., Phys. Rev. Lett. 94 (6), 65001 (2005)]. In the present work, similar behavior is found for double tearing modes (DTM) on resonant surfaces with q >= 1. A detailed analysis of linear instability characteristics of DTMs with various mode numbers m is performed using numerical simulations. The mode structures and dispersion relations for linearly unstable modes are calculated. Comparisons between low- and higher-m modes are carried out, and the roles of the inter-resonance distance and of the magnetic Reynolds number S_Hp are investigated. High-m modes are found to be destabilized when the distance between the resonant surfaces is small. They dominate over low-m modes in a wide range of S_Hp, including regimes relevant for tokamak operation. These results may be readily applied to configurations with more than two resonant surfaces.Comment: 11 pages, 15 figure

Classification of radiating compact stars

A classification of compact stars, depending on the electron distribution in velocity space and the density profiles characterizing their magnetospheric plasma, is proposed. Fast pulsars, such as NP 0532, X-ray sources such as Sco-X1, and slow pulsars are suggested as possible evolutionary stages of similar objects. The heating mechanism of Sco-X1 is discussed in some detail

Dynamics of resistive double tearing modes with broad linear spectra

The nonlinear evolution of resistive double tearing modes (DTMs) with safety factor values q=1 and q=3 is studied in a reduced cylindrical model of a tokamak plasma. We focus on cases where the resonant surfaces are a small distance apart. Recent numerical studies have shown that in such configurations high-m modes are strongly unstable. In this paper, it is first demonstrated that linear DTM theory predicts the dominance of high-m DTMs. A semi-empirical formula for estimating the poloidal mode number of the fastest growing mode, m_peak, is obtained from the existing linear theory. Second, using nonlinear simulations, it is shown that the presence of fast growing high-m modes leads to a rapid turbulent collapse in an annular region, whereby small magnetic island structures form. Furthermore, consideration is given to the evolution of low-m modes, in particular the global m=1 internal kink, which can undergo nonlinear driving through coupling to fast growing linear high-m DTMs. Factors influencing the details of the dynamics are discussed. These results may be relevant for the understanding of the magnetohydrodynamic (MHD) activity near the minimum of q and may thus be of interest to studies concerned with stability and confinement in advanced tokamaks.Comment: 11 pages, 10 figure

Thermo-Rotational Instability in Plasma Disks Around Compact Objects

Differentially rotating plasma disks, around compact objects, that are imbedded in a ``seed'' magnetic field are shown to develop vertically localized ballooning modes that are driven by the combined radial gradient of the rotation frequency and vertical gradients of the plasma density and temperature. When the electron mean free path is shorter than the disk height and the relevant thermal conductivity can be neglected, the vertical particle flows produced by of these modes have the effect to drive the density and temperature profiles toward the ``adiabatic condition'' where $\eta_{T}\equiv(dlnT/dz)/(dlnn/dz)=2/3$. Here $T$ is the plasma temperature and $n$ the particle density. The faster growth rates correspond to steeper temperature profiles $(\eta_{T}>2/3)$ such as those produced by an internal (e.g., viscous) heating process. In the end, ballooning modes excited for various values of $\eta_{T}$ can lead to the evolution of the disk into a different current carrying configuration such as a sequence of plasma rings

Theoretical Resolution of Magnetic Reconnection in High Energy Plasmas

The formation of macroscopic reconnected magnetic structures (islands) have been observed in advanced experiments on weakly collisional, well confined plasmas while established theories of the drift-tearing modes, which depend strongly on the electron temperature gradient and can describe the formation of these structures, had predicted practically inaccessible excitation thresholds for them in these regimes. The relevant theoretical dilemma is resolved as mesoscopic modes that depend critically on the ratio of the transverse (to the magnetic field) to the longitudinal thermal conductivity{D^e_{\perp}/D^e_{\|}, can produce large scale magnetic reconnection. These modes are envisioned to emerge from a background, which can be coherent, of collisionless microscopic reconnecting modes driven by the electron temperature gradient, that create a sequence of adjacent strings of magnetic islands and increase considerably the ratio {D^e_{\perp}/D^e_{\|} over its classical value. The mesoscopic reconnecting mode is treated by a singular perturbation analysis involving three asymptotic regions and the small parameters ${(D^e_{\perp}/D^e_{\|})}^{1/4}$ and ${\epsilon}^{1/4}_{*}$, where ${\epsilon}_{*} {\equiv}D_m/D_A$, $D_m$ is the magnetic diffusion coefficient, $D_A\sim\texttt{v}^{2}_{A}r_{Te}/(D_Bk_{\perp})$, $r_{Te}\equiv(-d\texttt{ln}T_e/dr)^{-1}$, $k_{\perp}$ is the transverse mode number, \texttt{v}^{2}_{A}=B^{2}/(4\pi{nm}_{i})} and $D_B=cT_e/(eB)$.Comment: To be published in "Collective Phenomena in Macroscopic Systems", Eds. G. Bertin, et al., Publ. World Scientific, 2007. Preprinted here with the permission of the editor

Interpretation of the I-Regime and transport associated with relevant heavy particle modes

The excitation of a novel kind of heavy particle [1, 2] mode at the edge of the plasma column is considered as the signature of the I-con nement Regime [3{7]. The outward transport of impurities produced by this mode is in fact consistent with the observed expulsion of them from the main body of the plasma column (a high degree of plasma purity is a necessary feature for fusion burning plasmas capable of approaching ignition). Moreover, the theoretically predicted mode phase velocity, in the direction of the electron diamagnetic velocity, has been con rmed by relevant experimental analyses [8] of the excited uctuations (around 200 kHz). The plasma \spontaneous rotation" in the direction of the ion diamagnetic velocity is also consistent, according to the Accretion Theory [9] of this phenomenon, with the direction of the mode phase velocity. Another feature of the mode that predicted by the theory is that the I-Regime exhibits a knee of the ion temperature at the edge of the plasma column but not one of the particle density as the mode excitation factor is the relative main ion temperature gradient exceeding the local relative density gradient. The net plasma current density appearing in the saturation stage of the relevant instability, where the induced particle and energy uxes are drastically reduced, is associated with the signi cant amplitudes of the poloidal magnetic eld uctuations [6, 7] observed to accompany the density uctuations. The theoretical implications of the signi cant electron temperature uctuations [10] observed are discussed.United States. Dept. of Energ

Reduced magnetohydrodynamic theory of oblique plasmoid instabilities

The three-dimensional nature of plasmoid instabilities is studied using the reduced magnetohydrodynamic equations. For a Harris equilibrium with guide field, represented by \vc{B}_o = B_{po} \tanh (x/\lambda) \hat{y} + B_{zo} \hat{z}, a spectrum of modes are unstable at multiple resonant surfaces in the current sheet, rather than just the null surface of the polodial field $B_{yo} (x) = B_{po} \tanh (x/\lambda)$, which is the only resonant surface in 2D or in the absence of a guide field. Here $B_{po}$ is the asymptotic value of the equilibrium poloidal field, $B_{zo}$ is the constant equilibrium guide field, and $\lambda$ is the current sheet width. Plasmoids on each resonant surface have a unique angle of obliquity $\theta \equiv \arctan(k_z/k_y)$. The resonant surface location for angle $\theta$ is x_s = - \lambda \arctanh (\tan \theta B_{zo}/B_{po}), and the existence of a resonant surface requires $|\theta| < \arctan (B_{po} / B_{zo})$. The most unstable angle is oblique, i.e. $\theta \neq 0$ and $x_s \neq 0$, in the constant-$\psi$ regime, but parallel, i.e. $\theta = 0$ and $x_s = 0$, in the nonconstant-$\psi$ regime. For a fixed angle of obliquity, the most unstable wavenumber lies at the intersection of the constant-$\psi$ and nonconstant-$\psi$ regimes. The growth rate of this mode is $\gamma_{\textrm{max}}/\Gamma_o \simeq S_L^{1/4} (1-\mu^4)^{1/2}$, in which $\Gamma_o = V_A/L$, $V_A$ is the Alfv\'{e}n speed, $L$ is the current sheet length, and $S_L$ is the Lundquist number. The number of plasmoids scales as $N \sim S_L^{3/8} (1-\mu^2)^{-1/4} (1 + \mu^2)^{3/4}$.Comment: 9 pages, 8 figures, to be published in Physics of Plasma

Active black holes: Relevant plasma structures, regimes and processes involving all phase space

The presented theory is motivated by the growing body of experimental information on the characteristics, connected with relevant spectral, time, and space resolutions, of the radiation emission from objects considered as rotating black holes. In the immediate surroundings of these objects, three plasma regions are identified: an innermost Buffer Region, an intermediate Three-regime Region, and a Structured Peripheral Region. In the last region, a Composite Disk Structure made of a sequence of plasma rings corresponding to the formation of closed magnetic surfaces is considered to be present and to allow intermittent accretion flows along the relevant separatrices. The nonlinear “Master Equation” describing composite disk structures is derived and solved in appropriate asymptotic limits. A ring configuration, depending on the state of the plasma at the microscopic level: (i) can be excluded from forming given the strongly nonthermal nature of the electron distribution (in momentum space) within the Three-regime Region allowing the onset of a spiral structure; the observed High Frequency Quasi Periodic Oscillations are associated with these tridimensional structures; (ii) may be allowed to propagate to the outer edge of the Buffer Region where successive rings carrying currents in opposite directions are ejected vertically (in opposite directions) and originate the observed jets; or (iii) penetrates in the Three-regime Region and is dissipated before reaching the outer edge of the Buffer Region. The absence of a coherent composite disk structure guiding accretion in the presence of a significant magnetic field background is suggested to characterize quiescent black holes.United States. Dept. of Energ

Comparison between resistive and collisionless double tearing modes for nearby resonant surfaces

The linear instability and nonlinear dynamics of collisional (resistive) and collisionless (due to electron inertia) double tearing modes (DTMs) are compared with the use of a reduced cylindrical model of a tokamak plasma. We focus on cases where two q = 2 resonant surfaces are located a small distance apart. It is found that regardless of the magnetic reconnection mechanism, resistivity or electron inertia, the fastest growing linear eigenmodes may have high poloidal mode numbers m ~ 10. The spectrum of unstable modes tends to be broader in the collisionless case. In the nonlinear regime, it is shown that in both cases fast growing high-m DTMs lead to an annular collapse involving small magnetic island structures. In addition, collisionless DTMs exhibit multiple reconnection cycles due to reversibility of collisionless reconnection and strong ExB flows. Collisionless reconnection leads to a saturated stable state, while in the collisional case resistive decay keeps the system weakly dynamic by driving it back towards the unstable equilibrium maintained by a source term.Comment: 15 pages, 9 figure

Induced scattering of short radio pulses

Effect of the induced Compton and Raman scattering on short, bright radio pulses is investigated. It is shown that when a single pulse propagates through the scattering medium, the effective optical depth is determined by the duration of the pulse but not by the scale of the medium. The induced scattering could hinder propagation of the radio pulse only if close enough to the source a dense enough plasma is presented. The induced scattering within the relativistically moving source places lower limits on the Lorentz factor of the source. The results are applied to the recently discovered short extragalactic radio pulse.Comment: submitted to Ap