Unrenormalizable Theories Can Be Predictive

Unrenormalizable theories contain infinitely many free parameters. Considering these theories in terms of the Wilsonian renormalization group (RG), we suggest a method for removing this large ambiguity. Our basic assumption is the existence of the maximal ultraviolet cutoff in a cutoff theory, and we require that the theory be so fine-tuned as to reach the maximal cutoff. The theory so obtained behaves as a local continuum theory to the shortest distance. In concrete examples of the scalar theory we find that at least in a certain approximation to the Wilsonian RG, this requirement enable us to make unique predictions in the infrared regime in terms of a finite number of independent parameters. Therefore, the method might provide a way for calculating quantum corrections in a low-energy effective theory of quantum gravity.Comment: 33 pages, TeX, 14 figure

Extra dimensions prefer large tan⁡β\tan\beta

Assuming that the recent result obtained from the Monte Carlo simulations on the nonperturbative existence of the pure SU(2) Yang-Mills theory in five dimensions can be applied to a more general class of higher-dimensional gauge theories, we derive the conditions imposed by the nontriviality requirement on the theories. We find that the supersymmetric grand unified theories with extra dimensions prefer a large value (\gsim 2) of $\tan\beta$ of the minimal supersymmetric standard model, in accord with today's possible observation of the Higgs particle at LEP2.Comment: 26 pages, TeX, 7 figure

Linear Gyrokinetic Analyses of ITG Modes and Zonal Flows in LHD with High Ion Temperature

Ion temperature (Ti) gradient modes (ITG modes) and zonal flows for high Ti discharges in the Large Helical Device (LHD) are investigated by linear gyrokinetic Vlasov simulation. In recent LHD experiments, high Ti plasmas are generated by neutral beam injection, and spatial profiles of density fluctuations are measured by phase contrast imaging (PCI) [K. Tanaka et al., Plasma Fusion Res. 5, S2053 (2010)]. The observed fluctuations most likely propagate in the direction of the ion diamagnetic rotation in the plasma frame, and their amplitudes increase with the growth of the temperature gradient. The results show the characteristics of ITG turbulence. To investigate the ITG modes and zonal flows in the experiment, linear gyrokinetic simulations were performed in the corresponding equilibria with different Ti profiles by using the GKV-X code [M. Nunami et al., Plasma Fusion Res. 5, 016 (2010)]. The simulation results predict unstable regions for the ITG modes in radial, wavenumber, and phase velocity spaces, in agreement with the PCI measurements. Thus, the fluctuations observed in the experiment are attributed to ITG instability. The responses of the zonal flows show clear contrasts in different field spectra that depend on the Ti profile and the radial position. In addition to the dependence on the field spectra, the zonal flow residual levels are enhanced by increasing the radial wavenumber as theoretically predicted

Reduced models of turbulent transport in helical plasmas including effects of zonal flows and trapped electrons

Using transport models, the impacts of trapped electrons on zonal flows and turbulence in helical field configurations are studied. The effect of the trapped electrons on the characteristic quantities of the linear response for zonal flows is investigated for two different field configurations in the Large Helical Device. The turbulent potential fluctuation, zonal flow potential fluctuation and ion energy transport are quickly predicted by the reduced models for which the linear and nonlinear simulation results are used to determine dimensionless parameters related to turbulent saturation levels and typical zonal flow wavenumbers. The effects of zonal flows on the turbulent transport for the case of the kinetic electron response are much smaller than or comparable to those in an adiabatic electron condition for the two different field configurations. It is clarified that the effect of zonal flows on the turbulent transport due to the trapped electrons changes, depending on the field configurations

繰り込み不可能理論における予言力と最大局所性

取得学位：博士(理学)，学位授与番号：博甲第611号，学位授与年月日：平成16年3月25日,学位授与年：200

Polarization and magnetization in collisional and turbulent transport processes

Expressions of polarization and magnetization in magnetically confined plasmas are derived, which include full expansions in the gyroradius to treat effects of both equilibrium and microscopic electromagnetic turbulence. Using the obtained expressions, densities and flows of particles are related to those of gyrocenters. To the first order in the normalized gyroradius expansion, the mean part of the particle flow is given by the sum of the gyrocenter flow and the magnetization flow, which corresponds to the so-called magnetization law in drift kinetics, while the turbulent part contains the polarization flow as well. Collisions make an additional contribution to the second-order particle flow. The mean particle flux across the magnetic surface is of the second-order, and it contains classical, neoclassical, and turbulent transport processes. The Lagrangian variational principle is used to derive the gyrokinetic Poisson and Ampère equations, which properly include mean and turbulent parts so as to be useful for full-f global electromagnetic gyrokinetic simulations. It is found that the second-order Lagrangian term given by the inner product of the turbulent vector potential and the drift velocity consisting of the curvature drift and the ∇B drift should be retained in order for the derived Ampère equation to correctly include the diamagnetic current, which is necessary especially for the full-f high-beta plasma simulations. The turbulent parts of these gyrokinetic Poisson and Ampère equations are confirmed to agree with the results derived from the WKB representation in earlier works

A Multi-Scale Electromagnetic Particle Code with Adaptive Mesh Refinement and Its Parallelization

AbstractSpace plasma phenomena occur in multi-scale processes from the electron scale to the magnetohydrodynamic scale. In order to investigate such multi-scale phenomena including plasma kinetic effects, we started to develop a new electromagnetic Particle-In-Cell (PIC) code with Adaptive Mesh Refinement (AMR) technique. AMR can realize high-resolution calculation saving computer resources by generating and removing hierarchical cells dynamically. In the parallelization, we adopt domain decomposition method and for good locality preserving and dynamical load balancing, we will use the Morton ordered curve. In the PIC method, particle calculation occupies most of the total calculation time. In our AMR-PIC code, time step intervals are also refined. To realize the load balancing between processes in the domain decomposition scheme, it is the most essential to consider the number of particle calculation loops for each cell among all hierarchical levels as a work weight for each processor. Therefore, we calculate the work weights based on the cost of particle calculation and hierarchical levels of each cell. Then we decompose the domain according to the Morton curve and the work weight, so that each processor has approximately the same amount of work. By performing a simple one-dimensional simulation, we confirmed that the dynamic load balancing is achieved and the computation time is reduced by introducing the dynamic domain decomposition scheme

Effects of collisions on conservation laws in gyrokinetic field theory

Effects of collisions on conservation laws for toroidal plasmas are investigated based on the gyrokinetic field theory. Associating the collisional system with a corresponding collisionless system at a given time such that the two systems have the same distribution functions and electromagnetic fields instantaneously, it is shown how the collisionless conservation laws derived from Noether\u27s theorem are modified by the collision term. Effects of the external source term added into the gyrokinetic equation can be formulated similarly with the collisional effects. Particle, energy, and toroidal momentum balance equations including collisional and turbulent transport fluxes are systematically derived using a novel gyrokinetic collision operator, by which the collisional change rates of energy and canonical toroidal angular momentum per unit volume in the gyrocenter space can be given in the conservative forms. The ensemble-averaged transport equations of particles, energy, and toroidal momentum given in the present work are shown to include classical, neoclassical, and turbulent transport fluxes which agree with those derived from conventional recursive formulations