2,281 research outputs found

    Non-thermal particle acceleration and power-law tails via relaxation to universal Lynden-Bell equilibria

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    Collisionless and weakly collisional plasmas often exhibit non-thermal quasi-equilibria. Among these quasi-equilibria, distributions with power-law tails are ubiquitous. It is shown that the statistical-mechanical approach originally suggested by Lynden-Bell (Mon. Not. R. Astron. Soc., vol. 136, 1967, p. 101) can easily recover such power-law tails. Moreover, we show that, despite the apparent diversity of Lynden-Bell equilibria, a generic form of the equilibrium distribution at high energies is a ‘hard’ power-law tail ∝ε−2, where ε is the particle energy. The shape of the ‘core’ of the distribution, located at low energies, retains some dependence on the initial condition but it is the tail (or ‘halo’) that contains most of the energy. Thus, a degree of universality exists in collisionless plasmas

    Spectral line shape of resonant four-wave mixing induced by broad-bandwidth lasers

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    We present a theoretical and experimental study of the line shape of resonant four-wave mixing induced by broad-bandwidth laser radiation that revises the theory of Meacher, Smith, Ewart, and Cooper (MSEC) [Phys. Rev. A 46, 2718 (1992)]. We adopt the same method as MSEC but correct for an invalid integral used to average over the distribution of atomic velocities. The revised theory predicts a Voigt line shape composed of a homogeneous, Lorentzian component, defined by the collisional rate Γ, and an inhomogeneous, Doppler component, which is a squared Gaussian. The width of the inhomogeneous component is reduced by a factor of √2 compared to the simple Doppler width predicted by MSEC. In the limit of dominant Doppler broadening, the width of the homogeneous component is predicted to be 4Γ, whereas in the limit of dominant homogeneous broadening, the predicted width is 2Γ. An experimental measurement is reported of the line shape of the four-wave-mixing signal using a broad-bandwidth, "modeless", laser resonant with the Q1 (6) line of the A2 Σ - X2 Π(0,0) system of the hydroxyl radical. The measured widths of the Voigt components were found to be consistent with the predictions of the revised theory

    Non-thermal particle acceleration and power-law tails via relaxation to universal Lynden-Bell equilibria

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    Collisionless and weakly collisional plasmas often exhibit non-thermal quasi-equilibria. Among these quasi-equilibria, distributions with power-law tails are ubiquitous. It is shown that the statistical-mechanical approach originally suggested by Lynden-Bell (1967) can easily recover such power-law tails. Moreover, we show that, despite the apparent diversity of Lynden-Bell equilibria, a generic form of the equilibrium distribution at high energies is a `hard' power-law tail ε2\propto \varepsilon^{-2}, where ε\varepsilon is the particle energy. The shape of the `core' of the distribution, located at low energies, retains some dependence on the initial condition but it is the tail (or `halo') that contains most of the energy. Thus, a degree of universality exists in collisionless plasmas.Comment: 33 pages, 5 figure

    Collisionless relaxation of a Lynden-Bell plasma

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    Plasmas whose Coulomb-collision rates are very small may relax on shorter time scales to non-Maxwellian quasi-equilibria, which, nevertheless, have a universal form, with dependence on initial conditions retained only via an infinite set of Casimir invariants enforcing phase-volume conservation. These are distributions derived by Lynden-Bell (1967) via a statistical-mechanical entropy-maximisation procedure, assuming perfect mixing of phase-space elements. To show that these equilibria are reached dynamically, one must derive an effective ‘collisionless collision integral’ for which they are fixed points—unique and inevitable provided the integral has an appropriate H-theorem. We describe how such collision integrals are derived and what assumptions are required for them to have a closed form, how to prove the H-theorems for them, and why, for a system carrying sufficiently large electric-fluctuation energy, collisionless relaxation should be fast. It is suggested that collisionless dynamics may favour maximising entropy locally in phase space before converging to global maximum-entropy states. Relaxation due to interspecies interaction is examined, leading, inter alia, to spontaneous transient generation of electron currents. The formalism also allows efficient recovery of ‘true’ collision integrals for both classical and quantum plasmas

    The effects of light pruning, irrigation and improved soil management on wine quality of the Vitis vinifera cv. Riesling

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    A number of yield improving viticultural practices were assessed in terms of their effect on wine quality. These were improved soil management, lighter pruning/higher trellis, irrigation and a control. In the first year a yield increase of 1.6 t /ha for the irrigation treatment had no significant effect on wine quality. A procedure is presented to assess judges for reliability, discrimination, variability and stability as part of analysis of the sensory results. Four judges were able to consistently identify lot differences

    Cognitive representations of disability behaviours in people with mobility limitations : consistency with theoretical constructs

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    Disability is conceptualised as behaviour by psychological theory and as a result of bodily impairment by medical models. However, how people with disabilities conceptualise those disabilities is unclear. The purpose of this study was to examine disability representations in people with mobility disabilities. Thirteen people with mobility disabilities completed personal repertory grids (using the method of triads) applied to activities used to measure disabilities. Ten judges with expertise in health psychology then examined the correspondence between the elicited disability constructs and psychological and medical models of disability. Participants with mobility disabilities generated 73 personal constructs ofdisability. These constructs were judged consistent with the content of two psychological models, namely the theory of planned behaviour and social cognitive theory and with the main medical model of disability, the International Classification of Functioning Disability and Health.Individuals with activity limitations conceptualise activities in a manner that is compatible with both psychological and medical models. This ensures adequate communication in contexts where the medical model is relevant, e.g. clinical contexts, as well as in everyday conversation about activities and behaviours. Finally, integrated models of disability may be of value for theory driven interdisciplinary approaches to disability and rehabilitation

    Phase-space entropy cascade and irreversibility of stochastic heating in nearly collisionless plasma turbulence

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    We consider a nearly collisionless plasma consisting of a species of `test particles' in 1D-1V, stirred by an externally imposed stochastic electric field. The mean effect on the particle distribution function is stochastic heating. Accompanying this heating is the generation of fine-scale structure in the distribution function, which we characterize with the collisionless (Casimir) invariant C2dxdvf2C_2 \propto \iint dx dv \, \langle f^2 \rangle. We find that C2C_2 is transferred from large scales to small scales in both position and velocity space via a phase-space cascade enabled by both particle streaming and nonlinear interactions between particles and the stochastic electric field. We compute the steady-state fluxes and spectrum of C2C_2 in Fourier space, with kk and ss denoting spatial and velocity wavenumbers, respectively. Whereas even the linear phase mixing alone would lead to a constant flux of C2C_2 to high ss (towards the collisional dissipation range) at every kk, the nonlinearity accelerates this cascade by intertwining velocity and position space so that the flux of C2C_2 is to both high kk and high ss simultaneously. Integrating over velocity (spatial) wavenumbers, the kk-space (ss-space) flux of C2C_2 is constant down to a dissipation length (velocity) scale that tends to zero as the collision frequency does, even though the rate of collisional dissipation remains finite. The resulting spectrum in the inertial range is a self-similar function in the (k,s)(k,s) plane, with power-law asymptotics at large kk and ss. We argue that stochastic heating is made irreversible by this entropy cascade and that, while collisional dissipation accessed via phase mixing occurs only at small spatial scales rather than at every scale as it would in a linear system, the cascade makes phase mixing even more effective overall in the nonlinear regime than in the linear one.Comment: 26 pages, 6 figure

    Efficient micromirror confinement of sub-TeV cosmic rays in galaxy clusters

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    Recent observations suggest a stronger confinement of cosmic rays (CRs) in certain astrophysical systems than predicted by current CR-transport theories. We posit that the incorporation of microscale physics into CR-transport models can account for this enhanced CR confinement. We develop a theoretical description of the effect of magnetic microscale fluctuations originating from the mirror instability on macroscopic CR diffusion. We confirm our theory with large-dynamical-range simulations of CR transport in the intracluster medium (ICM) of galaxy clusters and kinetic simulations of CR transport in micromirror fields. We conclude that sub-TeV CR confinement in the ICM is far more effective than previously anticipated on the basis of Galactic-transport extrapolations.Comment: Utilizes PIC and MHD simulations, complemented by deep learning for data analysis. Currently under journal review. Comments welcome
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