Poloidal Magnetic Field Energy Research Articles

Lower hybrid wave absorption study to improve the calculation of energy confinement time in EAST

The auxiliary heating power absorption of 2.45 GHz and 4.6 GHz lower hybrid (LH) waves in EAST is analysed in order to improve the determination of the energy confinement time. The LH power absorption coefficient is obtained by using the time derivative of the total stored energy including the plasma kinetic energy and the poloidal magnetic field energy. Results on EAST have shown that, for both frequencies, the fraction of LH power absorbed in the plasma bulk decreases with the increase in the plasma density, and with the decrease in the toroidal magnetic field. Scaling laws for the density dependence of the LH absorption coefficient at different fields and frequencies have been statistically obtained. Comparison of the confinement improvement factor H89 obtained with these new scaling laws against those assuming an absorption coefficient equal to the launched k//wave spectrum directivity is made.

Measurement and physical interpretation of the mean motion of turbulent density patterns detected by the beam emission spectroscopy system on the mega amp spherical tokamak

The mean motion of turbulent patterns detected by a two-dimensional beam emission spectroscopy (BES) diagnostic on the mega amp spherical tokamak (MAST) is determined using a cross-correlation time delay method. Statistical reliability of the method is studied by means of synthetic data analysis. The experimental measurements on MAST indicate that the apparent mean poloidal motion of the turbulent density patterns in the lab frame arises because the longest correlation direction of the patterns (parallel to the local background magnetic fields) is not parallel to the direction of the fastest mean plasma flows (usually toroidal when strong neutral-beam injection is present). This effect is particularly pronounced in a spherical tokamak because of the relatively large mean rotation and large magnetic pitch angle. The experimental measurements are consistent with the mean motion of plasma being toroidal. The sum of all other contributions (mean poloidal plasma flow, phase velocity of the density patterns in the plasma frame, non-linear effects, etc) to the apparent mean poloidal velocity of the density patterns is found to be negligible. These results hold in all investigated L-mode, H-mode and internal transport barrier discharges. The one exception is a high-poloidal-beta (the ratio of the plasma pressure to the poloidal magnetic field energy density) discharge, where a large magnetic island exists. In this case BES detects very little motion. This effect is currently theoretically unexplained.

Updated gravitational-wave upper limits on the internal magnetic field strength of recycled pulsars

Recent calculations of the hydromagnetic deformation of a stratified, non-barotropic neutron star are generalized to describe objects with superconducting interiors, whose magnetic permeability \mu is much smaller than the vacuum value \mu_0. It is found that the star remains oblate if the poloidal magnetic field energy is \gtrsim 40% of total magnetic field energy, that the toroidal field is confined to a torus which shrinks as \mu decreases, and that the deformation is much larger (by a factor \sim \mu_0/\mu) than in a non-superconducting object. The results are applied to the latest direct and indirect upper limits on gravitational-wave emission from Laser Interferometer Gravitational Wave Observatory (LIGO) and radio pulse timing (spin-down) observations of 81 millisecond pulsars, to show how one can use these observations to infer the internal field strength. It is found that the indirect spin-down limits already imply astrophysically interesting constraints on the poloidal-toroidal field ratio and diamagnetic shielding factor (by which accretion reduces the observable external magnetic field, e.g. by burial). These constraints will improve following gravitational-wave detections, with implications for accretion-driven magnetic field evolution in recycled pulsars and the hydromagnetic stability of these objects' interiors.

Ohmic Radio-Frequency Synergy Current Drive and TransformerRecharging Experiments in the HT-7 Tokamak

Lower hybrid current drive (LHCD) experiments for investigating theinteraction between lower hybrid (LH) wave and residual dc electric field wereperformed in extensive plasma parameter ranges in the HT-7superconducting tokamak. The experimental results are well fitted to theKarney–Fisch theory on the efficiency of LH waves energyconverted to poloidal magnetic field energy. The fraction of absorbed LHpower is about 0.75 for the HT-7 machine, and the upshift of the LH-waveparallel refraction index during LHCD experiments have been derived bythe optimizing fitting parameters. The LH wave is also used for thetransformer recharging when the plasma current is maintained unchanged.The highest efficiency about 7% has been achieved in HT-7 machine.

Theory and Astrophysical Consequences of a Magnetized Torus around a Rapidly Rotating Black Hole

We analyze the topology, lifetime, and emissions of a torus around a black hole formed in hypernovae and black hole-neutron star coalescence. The torus is ab initio uniformly magnetized, represented by two counteroriented current rings, and develops a state of suspended accretion against a magnetic wall around the black hole. Magnetic stability of the torus gives rise to a new fundamental limit /k < 0.1 for the ratio of poloidal magnetic field energy to kinetic energy, corresponding to a maximum magnetic field strength Bc (1016 G) (7 M☉/MH) (6MH/R)2 (MT/0.03MH)1/2. The lifetime of rapid spin of the black hole, effectively defined by the timescale of dissipation of spin energy Erot in the horizon, hereby satisfies T (40 s) (MH/7 M☉)(R/6MH)4(0.03MH/MT) for a black hole of mass MH surrounded by a torus of mass MT and radius R. The torus converts a major fraction Egw/Erot ~ 10% into gravitational radiation through a finite number of multipole mass moments and a smaller fraction into MeV neutrinos and baryon-rich winds. At a source distance of 100 Mpc, these emissions over N = 2 × 104 periods give rise to a characteristic strain amplitude N1/2hchar 6 × 10-21. We argue that torus winds create an open magnetic flux tube on the black hole, which carries a minor fraction Ej/Erot 10-3 in baryon-poor outflows to infinity. We conjecture that these are not high-σ outflows, owing, in part, to magnetic reconnection in surrounding current sheets. The fraction Ej/Erot ~ (MH/R)4 is standard for a universal horizon half-opening angle θH MH/R of the open flux tube. We identify this baryon-poor output of tens of seconds with gamma-ray bursts with contemporaneous and strongly correlated emissions in gravitational radiation, conceivably at multiple frequencies. Ultimately, this leaves a black hole binary surrounded by a supernova remnant.

Symmetries-imposed configurational limit and configurational limit-induced change of symmetry in an inductively driven, dissipative tokamak plasma

Hastie showed that, in a force-free tokamak configuration that encloses the magnetic axis, there exists a critical on-axis safety factor, q0, above which the q profile monotonically increases with radius and below which decreases with radius [J. Hastie, Nucl. Fusion 29, 96 (1989)]. This critical q0, when interpreted under the requirement of maximum poloidal magnetic field energy for an inductively driven, dissipative tokamak plasma, which does not allow dq/dr&amp;lt;0 for the toroidally symmetric configuration, becomes the onset condition of helical symmetry during current peaking in a sawtooth cycle. The value is a result of the opposing demands placed on the sign of the on-axis curvature of the safety factor, q″(0), by the two rotational symmetries (m=0 and n=0) of the configuration.

Turbulent steady-state configuration of an inductively driven, dissipative tokamak plasma

By taking Faraday’s equation into account and using a variational principle that optimizes dissipation, it is shown that the turbulent steady-state profile of current density of an inductively driven tokamak plasma is peaked at the axis and decreases monotonically to a finite value at the edge. It corresponds to a state of minimum rate of dissipation of poloidal magnetic field energy under the constraint that all tearing points on its rational surfaces are equally effective in reducing the slope of the current density across the surface. An alternative interpretation is that the configuration corresponds to a state of maximum poloidal magnetic field energy for the prescribed plasma current.

Calculation of βI and l i for three-dimensional plasma configurations

The Shafranov equilibrium formulas for tokamaks relate volume-averaged thermal pressure and magnetic pressure to integrals of the measurable poloidal magnetic field energy at the plasma surface. Similar integral relations are derived that are valid for a general, three-dimensional plasma confinement geometry.

Nonlinear dynamics of field maintenance and quasiperiodic relaxation in reversed-field pinches

The detailed dynamics underlying the self-generation of magnetic flux (‘‘dynamo’’) in reversed-field pinches (RFPs) is investigated with a three-dimensional magnetohydrodynamic code. A novel energy diagnostic is used to identify the path taken in Fourier space by the poloidal magnetic field energy as it is converted to axial magnetic field energy by the dynamo. At high values of the pinch parameter, Θ, and Lundquist number, S, the dynamo can be alternatingly dominated by quasilinear and nonlinear processes in a quasiperiodic fashion. Quasilinearly, the m=1 modes can reverse the axial field by themselves. However, m=0 modes are crucial to produce the nonlinear dynamo that triggers quasiperiodic relaxations. The same causal mechanism is likely to be responsible for the experimentally observed sawteeth.

Toroidal plasma current startup and sustainment by lower hybrid waves in the WT-3 tokamak

In WT-3, lower hybrid waves are injected into a microwave discharge at the electron cyclotron resonance frequency to initiate the toroidal plasma current IP and to sustain it by radiofrequency (RF) power alone without Ohmic heating power (this is called the ‘RF tokamak’). First, fast electrons in the range of several kilo-electronvolts are generated by electron cyclotron and lower hybrid power which initiate a weak toroidal plasma current. Then, fast electrons above 100 keV are produced by the lower hybrid waves, and IP increases rapidly (ΔIp/Δt ∼ 780 kA·s−1) to almost 13 kA. Subsequently the toroidal plasma current is ramped up slowly (ΔIp/Δt ∼ 180 kA·s−1) to > 25 kA for low densities (n̄e < 6 × 1018 m−3). The fraction ∈R (≤8%) of injected lower hybrid power is converted into poloidal magnetic field energy. For high densities (n̄e = (6−12) × 1018 m−3), a quasi-steady-state discharge is obtained with IP = 7−20 kA, and the figure of merit ηCD is about 0.05 × 1019 A·m−2·W−1. The experimental values of ∈R and ηCD are explained by the direct loss of fast electrons.

Toroidal plasma current startup and sustainment by RF in the WT-3 tokamak.

The toroidal plasma current is started up by rf power alone and is ramped up to above 20 kA in a low density plasma. The fraction eR of injected LHW power is converted into poloidal magnetic field energy and its maximum value is about 5 %. For high density cases, a quasi-steady state discharge is obtained and the figure of merit ηCD for steady current drive by LHW is about 0.04 × 1019 (A·m-2/W). The direct loss of fast electrons from the plasma is very large and results in the low eR and ηCD in our experiments.

Fast-wave current drive in the Irvine torus.

Steady-state electron currents were driven by fast waves with ${\ensuremath{\omega}}_{\mathrm{ci}}$\ensuremath{\ll}\ensuremath{\omega}\ensuremath{\ll}${\ensuremath{\omega}}_{\mathrm{ce}}$ in an initially current-free plasma in the Irvine Torus. Current direction was controlled by the fast-wave phased-array antenna. Low power experiments (l25 W) generated up to 1.3 A of electron current with a peak effeciency of \ensuremath{\eta}=InR/P\ensuremath{\simeq}(6\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}2}$ A/W)(${10}^{13}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$)m. Up to 14% of the wave energy was converted to poloidal magnetic field energy.

Comparison of the theory and the practice of lower-hybrid current drive.

The theory of rf-driven plasma currents is applied to the lower-hybrid experiments on the Princeton Large Torus, Princeton University, tokamak. Particular emphasis is placed on those experiments in which the plasma current was varying. The comparison between theory and experiment is made with respect to the efficiency with which rf energy was converted to poloidal magnetic field energy. Good agreement is found irrespective of whether the current was increasing, constant, or decreasing.

Mixing of plasma columns in a tokamak

The possibility of a new electrotechnical method of plasma heating in tokamak-like toroidal systems is discussed. The method is based on the use of the external poloidal magnetic field energy which was spent on the creation of equilibrium systems of a few separate toroidal columns with parallel currents. The energy of interaction of the separate currents transforms into plasma particle energy during the process of mixing of the plasma columns to form one column. Dissipation takes place because of the generation of a current layer, the reconnection of magnetic field lines and the change of the topological connection of the magnetic surfaces. Qualitative estimates are given of the power of heating and of final-state parameters.