Free-boundary plasma equilibria with toroidal plasma flows

Magnetohydrodynamic equilibrium schemes with toroidal plasma flows and the scrape-off layer are developed for the 'divertor-type' and 'limiter-type' free boundaries in the tokamak cylindrical coordinator. With a toroidal plasma flow, the flux functions are considerably different under the isentropic and isothermal assumptions. The effects of the toroidal flow on the magnetic axis shift are investigated. In a high beta plasma, the magnetic shift due to the toroidal flow are almost the same for both the isentropic and isothermal cases, and are about 0.04a0 (a0 is the minor radius) for M0=0.2 (the toroidal Alfvѐn Mach number on the magnetic axis). In addition, the X-point is slightly shifted upward by 0.0125 a0. But the magnetic axis and the X-point shift due to the toroidal flow may be neglected because M0 is usually less than 0.05 in a real tokamak. The effects of the toroidal flow on the plasma parameters are also investigated. The high toroidal flow shifts the plasma outward due to the centrifugal effect. Temperature profiles are noticeable different because the plasma temperature is a flux function in the isothermal case.

Figures of merit for stellarators near the magnetic axis

A new paradigm for rapid stellarator configuration design has been recently demonstrated, in which the shapes of quasisymmetric or omnigenous flux surfaces are computed directly using an expansion in small distance from the magnetic axis. To further develop this approach, here we derive several other quantities of interest that can be rapidly computed from this near-axis expansion. First, the $\boldsymbol {\nabla }\boldsymbol {B}$ and $\boldsymbol {\nabla }\boldsymbol {\nabla }\boldsymbol {B}$ tensors are computed, which can be used for direct derivative-based optimization of electromagnetic coil shapes to achieve the desired magnetic configuration. Moreover, if the norm of these tensors is large compared with the field strength for a given magnetic field, the field must have a short length scale, suggesting it may be hard to produce with coils that are suitably far away. Second, we evaluate the minor radius at which the flux surface shapes would become singular, providing a lower bound on the achievable aspect ratio. This bound is also shown to be related to an equilibrium beta limit. Finally, for configurations that are constructed to achieve a desired magnetic field strength to first order in the expansion, we compute the error field that arises due to second-order terms.

Modeling pulse profiles in X-Ray pulsars with accretion column

The pulse profiles of the radiation coming from X-ray pulsars with an accretion column were modeled. Gravitational lensing and redshift in the Schwarzschild metric, as well as the reflection of X-Ray photons from the surface of a neutron star, were taken into account. On the basis of the obtained pulse profiles an analysis of possible errors in the measurements of the luminosities of X-ray pulsars associated with the inability of the observer to correctly take into account the anisotropy in the radiation emerging from the neutron star, as well as the angles between the pulsar’s rotation axis, the magnetic axis and the line of sight, was carried out.

Magnetic well and Mercier stability of stellarators near the magnetic axis

We have recently demonstrated that by expanding in small distance from the magnetic axis compared with the major radius, stellarator shapes with low neoclassical transport can be generated efficiently. To extend the utility of this new design approach, here we evaluate measures of magnetohydrodynamic interchange stability within the same expansion. In particular, we evaluate the magnetic well, Mercier's criterion, and resistive interchange stability near a magnetic axis of arbitrary shape. In contrast to previous work on interchange stability near the magnetic axis, which used an expansion of the flux coordinates, here we use the ‘inverse expansion’ in which the flux coordinates are the independent variables. Reduced expressions are presented for the magnetic well and stability criterion in the case of quasisymmetry. The analytic results are shown to agree with calculations from the VMEC equilibrium code. Finally, we show that near the axis, Glasser, Greene and Johnson's stability criterion for resistive modes approximately coincides with Mercier's ideal condition.

On the Geometry of the X-ray emission from pulsars a consistent inclination and beaming solution for the Be/X-ray pulsar SXP 1062

ABSTRACT SXP 1062 is a long-period X-ray pulsar (XRP) with a Be optical companion located in the Small Magellanic Cloud. First discovered in 2010 from XMM–Newton data, it has been the target of multiple observational campaigns due to the seeming incongruity between its long spin period and recent birth. In our continuing modelling efforts to determine the inclination angle (i) and magnetic axis angle (θ) of XRPs, we have fitted 19 pulse profiles from SXP 1062 with our pulsar model, Polestar, including three consecutive Chandra observations taken during the trailing end of a Type I outburst. These fittings have resulted in most likely values of i = 76○ ± 2○ and θ = 40○ ± 9○. SXP 1062 mostly displays a stable double-peaked pulse profile with the peaks separated by roughly a third of a phase, but recently the pulsar has spun up and widened to a spacing of roughly half of a phase, yet the Polestar fits for i and θ remain constant. Additionally, we note a possible correlation between the X-ray luminosity and the separation of the peaks in the pulse profiles corresponding to the highest luminosity states.

Pulsed fraction of super-critical column accretion flows on to neutron stars: Modeling of ultraluminous X-ray pulsars

We calculate the pulsed fraction (PF) of the super-critical column accretion flows on to magnetized neutron stars (NSs), of which the magnetic axis is misaligned with the rotation axis, based on the simulation results by Kawashima et al. (2016, PASJ, 68, 83). Here, we solve the geodesic equation for light in the Schwarzschild spacetime in order to take into account the light-bending effect. The gravitational redshift and the relativistic Doppler effect from gas motions of the accretion columns are also incorporated. The pulsed emission appears since the observed luminosity, which exceeds the Eddington luminosity for the stellar-mass black holes, periodically changes via precession of the column caused by the rotation of the NS. The PF tends to increase as $\theta _{\rm obs}$ approaches to $\theta _{\rm B}$, where $\theta _{\rm obs}$ and $\theta _{\rm B}$ are the observer’s viewing angle and the polar angle of the magnetic axis measured from the rotation axis, respectively. The maximum PF is around 50%. Also, we find that the PF becomes less than 5% for $\theta _{\rm obs} \lesssim 5^\circ$ or for $\theta _{\rm B} \lesssim 5^\circ$. Our results are consistent with observations of ultraluminous X-ray pulsars (ULXPs) with few exceptions, since the ULXPs mostly exhibit the PF of $\lesssim 50$%. Our present study supports the hypothesis that the ULXPs are powered by the super-critical column accretion on to NSs.