We evaluate a number of simple, one-point phenomenological models for the decay of energy-containing eddies in magnetohydrodynamic (MHD) and hydrodynamic turbulence. The MHD models include. effects of cross helicity and Alfvdnic couplings associated with a constant mean magnetic field, based on physical effects well-described in the literature. The analytic structure of three separate MHD models is discussed. The single hydrodynamic model and several MHD models are compared against results from spectral-method simulations. The hydrodynamic model phenomenology has been previously verified against experiments in wind tunnels, and certain experimentally determined parameters in the model are satisfactorily reproduced by the present simulation. This agreement supports the suitability of our numerical calculations for examining MHD turbulence, where practical difficulties make it more difficult to study physical examples. When the triple-decorrelation time and effects of spectral anisotropy are properly taken into account, particular MHD models give decay rates that remain correct to within a factor of 2 for several energy-halving times. A simple model of this type is likely to be useful in a number of applications in space physics, astrophysics, and laboratory plasma physics where the approximate effects of turbulence need to be included.

We present evidence that anisotropy of low frequency plasma turbulence scales linearly with the ratio of fluctuating to total magnetic field strength for a useful range of parameters, for incompressible, weakly compressible, and driven magnetohydrodynamic turbulence. [S0031-9007(98) PACS numbers: 47.65. + a, 52.35.Ra, 95.30.Qd Evidence accumulated over the past several decades indicates that a large-scale applied (dc) magnetic field imposes a preferred direction on turbulence, and thus plays an important role in plasma diffusion [1], energetic particle scattering [2], and plasma heating [3][4][5]. Each of these in turn may significantly influence large-scale flows and structure [6][7][8]. The interplay between turbulence and large-scale magnetic field suggests a crucial role of rotational symmetry or "geometry" of the fluctuations in many astrophysical plasma settings. There has been considerable recent interest in detection and understanding of anisotropy of fluctuations in solar, interplanetary, and galactic plasmas, and thus it would appear to be of importance to understand mechanisms that can produce and regulate anisotropy in fluid-scale plasma turbulence. In this Letter we show, using numerical solutions of magnetohydrodynamics (MHD), that anisotropy produced by spectral transfer scales in a systematic way with applied field strength. In particular, an angular measure of the anisotropy of the spectrum varies linearly with field strength over a useful range of applied field magnitudes. A simple argument, based upon the physics of reduced MHD [9][10][11], explains this scaling property as well as its saturation.Within the MHD framework, anisotropy associated with a (uniform) dc magnetic field ͑B 0 ͒ may take a number of forms [12][13][14]. Here we are concerned specifically with dynamical development of spectral anisotropy due to asymmetry of nonlinear spectral transfer relative to the mean field direction [14,15]. This anisotropy is characterized by gradients across the mean magnetic field that are relatively larger than gradients along the field. Such features can be readily observed in fluctuations of plasma fluid velocity, magnetic field, and density, and have been observed in the solar wind [16][17][18], the solar corona [19], the interstellar medium [20,21], and in various laboratory plasma devices [22,23]. The limiting case, when all variations are perpendicular to the mean field, and the parallel coordinate is ignorable, is known as two-dimensional (2D) turbulence. The opposite limit, with perpendicular coordinates ignorable, often called "slab" symmetry, is traditionally employed in linear wave theory [2,16]. Turbulence that is "quasi-2D" is described by "reduced" MHD equations that emerge naturally in the theory of nearly incompressible MHD [24] for low plasma b.It is well known that anisotropy can be generated robustly through rapid turbulent wave-vector-space spectral transfer in the directions transverse to the mean field [14]. Parallel spectral transfer is relatively suppressed, so the spe...

No abstract

It is shown numerically, both for the two-dimensional Navier-Stokes (guidingcentre plasma) equations and for two-dimensional magnetohydrodynamics, that the long-time asymptotic state in a forced inverse-cascade situation is one in which the spectrum is completely dominated by its own fundamental. The growth continues until the fundamental is dissipatively limited by its own dissipation rate.

Three-dimensional incompressible hydrodynamic turbulence is driven to a statistically steady state. A strong uniform rotation is then turned on. It is shown that the turbulence reduces to an approximate two-dimensional state. Furthermore, the energy inverse cascades to longer length scales.

The purpose of this study is to characterize and understand the long‐term behavior of the output from megavoltage radiotherapy linear accelerators. Output trends of nine beams from three linear accelerators over a period of more than three years are reported and analyzed. Output, taken during daily warm‐up, forms the basis of this study. The output is measured using devices having ion chambers. These are not calibrated by accredited dosimetry laboratory, but are baseline‐compared against monthly output which is measured using calibrated ion chambers. We consider the output from the daily check devices as it is, and sometimes normalized it by the actual output measured during the monthly calibration of the linacs. The data show noisy quasi‐periodic behavior. The output variation, if normalized by monthly measured “real’ output, is bounded between ± 3%. Beams of different energies from the same linac are correlated with a correlation coefficient as high as 0.97, for one particular linac, and as low as 0.44 for another. These maximum and minimum correlations drop to 0.78 and 0.25 when daily output is normalized by the monthly measurements. These results suggest that the origin of these correlations is both the linacs and the daily output check devices. Beams from different linacs, independent of their energies, have lower correlation coefficient, with a maximum of about 0.50 and a minimum of almost zero. The maximum correlation drops to almost zero if the output is normalized by the monthly measured output. Some scatter plots of pairs of beam output from the same linac show band‐like structures. These structures are blurred when the output is normalized by the monthly calibrated output. Fourier decomposition of the quasi‐periodic output is consistent with a 1/f power law. The output variation appears to come from a distorted normal distribution with a mean of slightly greater than unity. The quasi‐periodic behavior is manifested in the seasonally averaged output, showing annual variability with negative variations in the winter and positive in the summer. This trend is weakened when the daily output is normalized by the monthly calibrated output, indicating that the variation of the periodic component may be intrinsic to both the linacs and the daily measurement devices. Actual linac output was measured monthly. It needs to be adjusted once every three to six months for our tolerance and action levels. If these adjustments are artificially removed, then there is an increase in output of about 2%–4% per year.PACS numbers: 87.56bd, 87.56Fc, 87.55Qr

Intensity modulated radiation therapy (IMRT) has stirred considerable excitement in the radiation oncology community. Its objective is to make the dose conform to the tumor and spare other organs. Instead of resorting to the rather complex inverse-planning, the technique described here is an extension of the conventional treatment planning technique. The beam orientation and wedge angles are chosen in the conventional rule-based manner. However, within each conformal beam's eye view (BEV) field including margin, a number of sub-field openings are added. The smaller field openings are designed to irradiate the tumor, while sparing the normal tissue of the organs at risk (OARs) that intrude into the target region in the BEV. As the number of intrusions into the target BEV increases, the number of sub-fields for each beam increases. The Cimmino simultaneous projection method was employed to obtain the optimized weighting for each field of each beam. In cases where the dose constraints for the tumor and for the OARs are reasonable, it is possible to obtain a plan with a fairly small number of beams that satisfies the specified dose objectives. This is illustrated for the treatment of prostate cancer, where the rectum creates a concavity in the planning target volume. An advantage of this technique is that the quality assurance for the delivery of these plans does not require extensive special efforts.

Three-dimensional (3D) turbulence is characterized by a dual forward cascade of both kinetic energy and helicity, a second inviscid flow invariant, from the integral scale of motion to the viscous dissipative scale. In helical flows, however, such as strongly rotating flows with broken mirror symmetry, an inverse energy cascade can be observed analogous to that of two-dimensional turbulence (2D) where a second positive-definite flow invariant, enstrophy, unlike helicity in 3D, effectively blocks the forward cascade of energy. In the spectral-helical decomposition of the Navier-Stokes equation it has previously been show that a subset of three-wave (triad) interactions conserve helicity in 3D in a fashion similar to enstrophy in 2D, thus leading to a 2D-like inverse energy cascade in 3D. In this work, we show both theoretically and numerically that an additional subset of interactions exist conserving a new pseudo-invariant in addition to energy and helicity, which contributes either to a forward or inverse energy cascade depending on the specific triad interaction geometry. Fully developed three-dimensional (3D) turbulence is char-acterised by a forward cascade of kinetic energy from the large integral scale of motion to the small Kolmogorov scale of viscous dissipation. In the large Reynolds number limit, η → 0, the production of enstrophy, the integral of the vor-ticity squared, by the stretching and bending term in the in-compressible Navier-Stokes equations (NSE) permits the vis-cous dissipation of energy at the Kolmogorov scale. In two-dimensional (2D) turbulence, the stretching and bending term is absent, and enstrophy is, in addition to energy, also an invis-cid invariant [1]. In this case, the dissipation of enstrophy prevents a simultaneous dissipation of energy at the Kolmogorov scale, effectively blocking the forward cascade of energy. The dual inviscid conservation of both quantities, E(k)dk and k 2 E(k)dk, the integrals over the spectral energy and enstro-phy densities, consequently implies a reversal of the energy cascade to larger scales (inverse cascade). In 3D turbulence, helicity, the integral of the scalar product of velocity and vor-ticity, is also an inviscid invariant [2]. Similarly to the enstro-phy spectrum, the helicity spectrum H(k) ∼ kE(k) dominates over the energy spectrum at small scales (large k), but unlike enstrophy, helicity is not sign definite. As a consequence, the increased dissipation of both signs of helicity compared to energy can be obtained without a net helicity production as long as the dissipation of both positive and negative helicities balance [3]. Inviscid conservation of helicity does therefore not prevent a forward cascade of energy [4]. In helical flows, however, such as strongly rotating flows with broken mirror symmetry, a simultaneous forward helic-ity cascade and inverse energy cascade can be observed [5]. In the spectral decomposition of the NSE, energy and helicity (and enstrophy in 2D) are conserved within each three-wave interaction (triad interaction). ...