# Matt Landreman - Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, USA

## Contact Details

NameMatt Landreman |
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AffiliationInstitute for Research in Electronics and Applied Physics, University of Maryland, College Park, USA |
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CityCollege Park |
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CountryUnited States |
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## Pubs By Year |
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## Pub CategoriesPhysics - Plasma Physics (17) Physics - Computational Physics (3) Mathematics - Numerical Analysis (1) |

## Publications Authored By Matt Landreman

Several fast methods for computing stellarator coil shapes are compared, including the classical NESCOIL procedure [Merkel, Nucl. Fusion 27, 867 (1987)], its generalization using truncated singular value decomposition, and a Tikhonov regularization approach we call REGCOIL in which the squared current density is included in the objective function. Considering W7-X and NCSX geometries, and for any desired level of regularization, we find the REGCOIL approach simultaneously achieves lower surface-averaged and maximum values of both current density (on the coil winding surface) and normal magnetic field (on the desired plasma surface). Read More

The velocity-space distribution of alpha particles born in fusion devices is subject to modification at moderate energies due to turbulent transport. Therefore, one must calculate the evolution of an equilibrium distribution whose functional form is not known \emph{a priori}. Using a novel technique, applicable to any trace impurity, we have made this calculation not only possible, but particularly efficient. Read More

The magnetic field that supports tokamak and stellarator plasmas must be produced by coils well separated from the plasma. However the larger the separation, the more difficult it is to produce a given magnetic field in the plasma region, so plasma configurations should be chosen that can be supported as efficiently as possible by distant coils. The efficiency of an externally-generated magnetic field is a measure of the field's shaping component magnitude at the plasma compared to the magnitude near the coils; the efficiency of a plasma equilibrium can be measured using the efficiency of the required external shaping field. Read More

**Authors:**Albert Mollén

^{1}, Matt Landreman

^{2}, Håkan M. Smith

^{3}, Stefanie Braun

^{4}, Per Helander

^{5}

**Affiliations:**

^{1}Department of Applied Physics, Chalmers University of Technology, Göteborg, Sweden,

^{2}Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, USA,

^{3}Max-Planck-Institut für Plasmaphysik, Greifswald, Germany,

^{4}Max-Planck-Institut für Plasmaphysik, Greifswald, Germany,

^{5}Max-Planck-Institut für Plasmaphysik, Greifswald, Germany

**Category:**Physics - Plasma Physics

Impurities cause radiation losses and plasma dilution, and in stellarator plasmas the neoclassical ambipolar radial electric field is often unfavorable for avoiding strong impurity peaking. In this work we use a new continuum drift-kinetic solver, the SFINCS code (the Stellarator Fokker-Planck Iterative Neoclassical Conservative Solver) [M. Landreman et al. Read More

In this work we numerically demonstrate both significant transient (i.e. non-modal) linear amplification and sustained nonlinear turbulence in a kinetic plasma system with no unstable eigenmodes. Read More

We demonstrate that the universal mode driven by the density gradient in a plasma slab can be absolutely unstable even in the presence of reasonable magnetic shear. Previous studies from the 1970s that reached the opposite conclusion used an eigenmode equation limited to $L_x \gg \rho_i$, where $L_x$ is the scale length of the mode in the radial direction, and $\rho_i$ is the ion Larmor radius. Here we instead use a gyrokinetic approach which does not have this same limitation. Read More

A stellarator is said to be omnigeneous if all particles have vanishing average radial drifts. In omnigeneous stellarators, particles are perfectly confined in the absence of turbulence and collisions, whereas in non-omnigeneous configurations, particle can drift large radial distances. One of the consequences of omnigeneity is that the unfavorable inverse scaling with collisionality of the stellarator neoclassical fluxes disappears. Read More

We examine the merits of using a family of polynomials that are orthogonal with respect to a non-classical weight function to discretize the speed variable in continuum kinetic calculations. We consider a model one-dimensional partial differential equation describing energy diffusion in velocity space due to Fokker-Planck collisions. This relatively simple case allows us to compare the results of the projected dynamics with an expensive but highly accurate spectral transform approach. Read More

In this work, we examine the validity of several common simplifying assumptions used in numerical neoclassical calculations for nonaxisymmetric plasmas, both by using a new continuum drift-kinetic code and by considering analytic properties of the kinetic equation. First, neoclassical phenomena are computed for the LHD and W7-X stellarators using several versions of the drift-kinetic equation, including the commonly used incompressible-ExB-drift approximation and two other variants, corresponding to different effective particle trajectories. It is found that for electric fields below roughly one third of the resonant value, the different formulations give nearly identical results, demonstrating the incompressible ExB-drift approximation is quite accurate in this regime. Read More

Conventional radially-local neoclassical calculations become inadequate if the radial gradient scale lengths of the H-mode pedestal become as small as the poloidal ion gyroradius. Here, we describe a radially global $\delta f$ continuum code that generalizes neoclassical calculations to allow stronger gradients. As with conventional neoclassical calculations, the formulation is time-independent and requires only the solution of a single sparse linear system. Read More

Poloidal asymmetries in the impurity density can be generated by radio frequency heating in the core and by neoclassical effects in the edge of tokamak plasmas. In a pedestal case study, using global neoclassical simulations we find that finite orbit width effects can generate significant poloidal variation in the electrostatic potential, which varies on a small radial scale. Gyrokinetic modeling shows that these poloidal asymmetries can be strong enough to significantly modify turbulent impurity peaking. Read More

Synchrotron emission from runaway electrons may be used to diagnose plasma conditions during a tokamak disruption, but solving this inverse problem requires rapid simulation of the electron distribution function and associated synchrotron emission as a function of plasma parameters. Here we detail a framework for this forward calculation, beginning with an efficient numerical method for solving the Fokker-Planck equation in the presence of an electric field of arbitrary strength. The approach is continuum (Eulerian), and we employ a relativistic collision operator, valid for arbitrary energies. Read More

Numerical techniques for discretization of velocity space in continuum kinetic calculations are described. An efficient spectral collocation method is developed for the speed coordinate - the radius in velocity space - employing a novel set of non-classical orthogonal polynomials. For problems in which Fokker-Planck collisions are included, a common situation in plasma physics, a procedure is detailed to accurately and efficiently treat the field term in the collision operator (in the absence of gyrokinetic corrections). Read More

In transport barriers, particularly H-mode edge pedestals, radial scale lengths can become comparable to the ion orbit width, causing neoclassical physics to become radially nonlocal. In this work, the resulting changes to neoclassical flow and current are examined both analytically and numerically. Steep density gradients are considered, with scale lengths comparable to the poloidal ion gyroradius, together with strong radial electric fields sufficient to electrostatically confine the ions. Read More

In a tokamak pedestal, radial scale lengths can become comparable to the ion orbit width, invalidating conventional neoclassical calculations of flow and bootstrap current. In this work we illustrate a non-local approach that allows strong radial density variation while maintaining small departures from a Maxwellian distribution. Non-local effects alter the magnitude and poloidal variation of the flow and current. Read More

Any viable stellarator reactor will need to be nearly omnigenous, meaning the radial guiding-center drift velocity averages to zero over time for all particles. While omnigenity is easier to achieve than quasisymmetry, we show here that several properties of quasisymmetric plasmas also apply directly or with only minor modification to the larger class of omnigenous plasmas. For example, concise expressions exist for the flow and current, closely resembling those for a tokamak, and these expressions are explicit in that no magnetic differential equations remain. Read More

In the standard "monoenergetic" approach to numerical calculation of stellarator neoclassical transport, to expedite computation, ad-hoc changes are made to the kinetic equation so speed enters only as a parameter. Here we examine the validity of this approach by considering the effective particle trajectories in a model magnetic field. We find monoenergetic codes systematically under-predict the true trapped particle fraction, with the error in the trapped ion fraction being of order unity when the electric field is large, suggesting some results of these codes may be unreliable in this regime. Read More

We show that in perfectly quasi-isodynamic magnetic fields, which are generally non-quasisymmetric and which can approximate fields of experimental interest, neoclassical calculations can be carried out analytically more completely than in a general stellarator. Here, we define a quasi-isodynamic field to be one in which the longitudinal adiabatic invariant is a flux function and in which the constant-B contours close poloidally. We first derive several geometric relations among the magnetic field components and the field strength. Read More