arXiv subjects

Rahul Gaur

Publications and source records attributed to Rahul Gaur.

13 recordsLinked to original sources

arXiv2026

AGNI: A differentiable MHD stability solver & optimizer for magnetic confinement fusion devices

The existence of an ideal MagnetoHydroDynamic (MHD) equilibrium does not guarantee its stability. Finite toroidal mode number (n) instabilities degrade performance in both tokamaks and stellarators and differentiable stability optimization tools to date have operated only in the infinite-n limit. We present AGNI (Analysis of Global Normal modes in Ideal MHD), a GPU-accelerated, automatically differentiable finite-n ideal MHD stability solver and optimizer. AGNI discretizes the ideal MHD energy principle pseudospectrally in real space using differentiation matrices and geometric coefficients from a DESC equilibrium, giving a variational eigenvalue problem for the plasma displacement, and efficiently finds the most unstable modes. Built on JAX, AGNI yields reverse-mode gradients of the growth rate with respect to boundary-shape and profile parameters without re-solving the equilibrium. We benchmark AGNI against the initial-value code NIMSTELL for a modified Landreman-Buller-Drevlak quasi-helically symmetric equilibrium, recovering the dominant m = n = 4 interchange mode with agreement in both growth rate and eigenfunction structure, and verify the automatic differentiation gradients against central finite differences. We quantify CPU and GPU cost for eigenvalue and gradient evaluation, establish the finite-precision limit on resolving near-marginal eigenvalues, and present a robust scheme to impose incompressibility compatible with gradient-based optimization. AGNI will allow us to optimize tokamaks, stellarators, and mirrors against ideal MHD instabilities.

physics.plasm-ph↗

arXiv2025

Surface Current Optimization and Coil-Cutting Algorithms for Stage-Two Stellarator Optimization

Stellarator optimization often takes a two-stage approach, where in the first stage the boundary is varied in order to optimize for some physics metrics, while in the second stage the boundary is kept fixed and coils are sought to generate a magnetic field that can recreate the desired stellarator. Past literature dealing with this stage lacks details on the coil cutting procedure and the mathematical and physical properties of the surface current potential which dictates it. In this work, some basic physical quantities of the surface current and how they relate to the parameters in the current potential are presented, and supported for the first time by explicit mathematical derivations. Additionally, the details of how to account for the presence of an external field in the surface current algorithm are explicitly presented. These relations underpin the procedure of discretizing the surface current into coils. Finally, the conventionally-used algorithm for discretizing the surface current into coils is detailed, along with an example coil optimization for both a modular and a helical coilset. The algorithm is implemented in the \texttt{DESC} code, with both modular and helical coil capabilities, where it is available for use in stellarator coil design.

physics.plasm-ph↗

arXiv2025

Optimizing stellarators with hidden symmetry

Stellarators confine fusion plasmas using three-dimensional magnetic fields composed of nested toroidal magnetic surfaces. In generic stellarators, trapped particles can drift across these surfaces and degrade plasma confinement. Certain topological properties of the magnetic field strength can suppress these drifts. However, conventional stellarator design approaches typically enforce restrictive constraints to realize such properties, thereby segmenting and limiting the accessible configuration space. In this work, we reformulate the conditions for efficient confinement as constraints on a homeomorphic straightening transformation of the field contours. Within this framework, the various families of stellarator magnetic fields optimized for plasma confinement arise naturally as specific realizations of a unified mapping. This new perspective provides a significantly more comprehensive description of viable stellarator configurations, enabling systematic exploration of trade-offs among confinement quality, geometric complexity, and engineering requirements. We illustrate this approach by presenting a highly compact stellarator design that nevertheless achieves plasma performance comparable to that of leading reactor-scale designs with much larger aspect ratios.

physics.plasm-ph↗

arXiv2024

Spectrally accurate, reverse-mode differentiable bounce-averaging algorithm and its applications

We present a fast, spectrally (exponentially) accurate, automatically differentiable bounce-averaging algorithm that is used to simplify kinetic models. Using this algorithm, implemented in the DESC stellarator optimisation suite, we can perform efficient optimisation of many objectives to improve stellarator performance, such as the effective ripple $\epsilon_{\mathrm{eff}}$ metric for the neoclassical transport coefficient in the low collisionality regime, energetic particle confinement, and turbulent transport. For the first time, we optimise a finite-beta stellarator to directly reduce neoclassical ripple transport using reverse-mode differentiation. This ensures the computational cost of differentiation is independent of the number of controllable parameters.

physics.plasm-ph↗

arXiv2024

Omnigenous stellarator equilibria with enhanced stability

To build an economically viable stellarator, it is essential to find a configuration that satisfies a set of favorable properties to achieve efficient steady-state nuclear fusion. One such property is omnigenity, which ensures confinement of trapped particles. After creating an omnigenous equilibrium, one must also ensure reduced transport resulting from kinetic and magnetohydrodynamic (MHD) instabilities. This study introduces and leverages the GPU-accelerated DESC optimization suite, which is used to design stable high-$\beta$ omnigenous equilibria, achieving Mercier, ideal ballooning, and enhanced kinetic ballooning stability. We explain the link between ideal and kinetic ballooning modes and discover stellarators with second stability, a regime of large pressure gradient where an equilibria becomes ideal ballooning stable.

physics.plasm-ph↗

arXiv2024

Effect of insulator end cap thickness on time-dependent Hartmann flow in a rotating mirror

We present a framework for analyzing plasma flow in a rotating mirror. By making a series of physical assumptions, we reduce the magnetohydrodynamic (MHD) equations in a three-dimensional cylindrical system to a one-dimensional system in a shallow, cuboidal channel within a transverse magnetic field, similar to the Hartmann flow in the ducts. We then solve the system both numerically and analytically for a range of values of the Hartmann number and calculate the dependence of the plasma flow speed on the thickness of the insulating end cap. We observe that the mean flow overshoots and decelerates before achieving a steady-state value, a phenomenon that the analytical model cannot capture. This overshoot is directly proportional to the thickness of the insulating end cap and the external electric field, with a weak dependence on the external magnetic field. Our simplified model can act as a benchmark for future simulations of the supersonic mirror device Compact Magnetic Fusion Experiment (CMFX), which will employ more sophisticated physics and realistic magnetic field geometries.

physics.plasm-ph↗

arXiv2024

A family of quasi-axisymmetric stellarators with varied rotational transform

We apply a continuation method to recently optimized stellarator equilibria with excellent quasi-axisymmetry (QA) to generate new equilibria with a wide range of rotational transform profiles. Using these equilibria, we investigate how the rotational transform affects fast-particle confinement, the maximum coil-plasma distance, the maximum growth rate in linear gyrokinetic ion-temperature gradient (ITG) simulations, and the ion heat flux in corresponding nonlinear simulations. We find values of two-term quasisymmetry error comparable to or lower than the similar Landreman-Paul (Phys. Rev. Lett. 128, 035001) configuration for values of the mean rotational transform $\bar{\iota}$ between $0.12$ and $0.75$. The fast-particle confinement improves with $\bar{\iota}$ until $\bar{\iota} = 0.73$, at which point the degradation in quasisymmetry outweighs the benefits of further increasing $\bar{\iota}$. The required coil-plasma distance only varies by about $\pm 10\%$ for the configurations under consideration, and is between $2.8\,\mathrm{m}$ to $3.3\,\mathrm{m}$ when the configuration is scaled up to reactor size. The maximum growth rate from linear gyrokinetic simulations increases with $\bar{\iota}$, but also shifts towards higher $k_y$ values. The maximum linear growth rate is sensitive to the choice of flux tube at rational $\iota$, but this can be compensated for by taking the maximum over several flux tubes. The corresponding ion heat fluxes from nonlinear simulations display a non-monotonic relation to $\iota$. Sufficiently large positive shear is destabilizing. This is reflected both in linear growth rates and nonlinear heat fluxes.

physics.plasm-ph↗

arXiv2023

Grad-Shafranov equilibria via data-free physics informed neural networks

A large number of magnetohydrodynamic (MHD) equilibrium calculations are often required for uncertainty quantification, optimization, and real-time diagnostic information, making MHD equilibrium codes vital to the field of plasma physics. In this paper, we explore a method for solving the Grad-Shafranov equation by using Physics-Informed Neural Networks (PINNs). For PINNs, we optimize neural networks by directly minimizing the residual of the PDE as a loss function. We show that PINNs can accurately and effectively solve the Grad-Shafranov equation with several different boundary conditions. We also explore the parameter space by varying the size of the model, the learning rate, and boundary conditions to map various trade-offs such as between reconstruction error and computational speed. Additionally, we introduce a parameterized PINN framework, expanding the input space to include variables such as pressure, aspect ratio, elongation, and triangularity in order to handle a broader range of plasma scenarios within a single network. Parametrized PINNs could be used in future work to solve inverse problems such as shape optimization.

physics.plasm-ph↗

arXiv2023

Optimization of Nonlinear Turbulence in Stellarators

We present new stellarator equilibria that have been optimized for reduced turbulent transport using nonlinear gyrokinetic simulations within the optimization loop. The optimization routine involves coupling the pseudo-spectral GPU-native gyrokinetic code GX with the stellarator equilibrium and optimization code DESC. Since using GX allows for fast nonlinear simulations, we directly optimize for reduced nonlinear heat fluxes. To handle the noisy heat flux traces returned by these simulations, we employ the simultaneous perturbation stochastic approximation (SPSA) method that only uses two objective function evaluations for a simple estimate of the gradient. We show several examples that optimize for both reduced heat fluxes and good quasisymmetry as a proxy for low neoclassical transport. Finally, we run full transport simulations using the T3D stellarator transport code to evaluate the changes in the macroscopic profiles.

physics.plasm-ph↗

arXiv2023

An adjoint-based method for optimizing MHD equilibria against the infinite-n, ideal ballooning mode

We demonstrate a fast adjoint-based method to optimize tokamak and stellarator equilibria against a pressure-driven instability known as the infinite-$n$ ideal ballooning mode. We present three finite-$\beta$ (the ratio of thermal to magnetic pressure) equilibria: one tokamak equilibrium and two stellarator equilibria that are unstable against the ballooning mode. Using the self-adjoint property of ideal MHD, we construct a technique to rapidly calculate the change in the growth rate, a measure of ideal ballooning instability. Using the~\texttt{SIMSOPT} framework, we then implement our fast adjoint gradient-based optimizer to minimize the growth rate and find stable equilibria for each of the three initially unstable equilibria.

physics.plasm-ph↗

arXiv2022

Microstability of $\beta \sim 1$ tokamak equilibria

High-power-density tokamaks offer a potential solution to design cost-effective fusion devices. One way to achieve high power density is to operate at a high $\beta$ value (the ratio of thermal to magnetic pressure), i.e., $\beta \sim 1$. However, a $\beta \sim 1$ state may be unstable to various pressure- and current-driven instabilities or have unfavorable microstability properties. To explore these possibilities, we generate $\beta \sim 1$ equilibria and investigate their stability. Initially, we study an analytical technique that was used in the past to generate $\beta \sim 1$ equilibria and outline its limitations. Hence, we demonstrate the generation of high-$\beta$ equilibria with the computer code $\texttt{VMEC}$. We then analyze these equilibria to determine their stability against the infinite-$n$ ideal ballooning mode. We follow that by engaging in a detailed microstability study, beginning with assessments of electrostatic ITG and TEM instabilities. We observe interesting behavior for the high-$\beta$ equilibria -- stabilization of these modes through two distinct mechanisms. Finally, we perform electromagnetic gyrokinetic simulations and again observe stabilizing trends in the equilibria at high $\beta$. These trends are different from their lower $\beta$ counterparts and offer an alternative, potentially favorable regime of tokamak operation.

physics.plasm-ph↗

arXiv2016

Reference Physics Design for 1 GeV Injector Linac and Accumulator Ring for Indian Spallation Neutron Source

As a part of the ongoing XIIth plan project titled "R&D activities for high energy proton linac based spallation neutron source", the work on physics design of various subsystems of the injector linac and accumulator ring has been taken up at RRCAT, Indore. For the 1 GeV H- injector linac, physics design studies of individual systems have been completed, and the end to end beam dynamics simulation studies have been performed to ensure that the stringent beam dynamics criteria are satisfied for the optimized lattice. Physics design studies to optimize the linear lattice of the accumulator ring have also been completed. The design studies for the beam transport lines from the injector linac to the accumulator ring, and from the accumulator ring to target are currently in progress. This report describes the physics design of various systems of the injector linac and the accumulator ring.

physics.acc-ph↗

arXiv2012

Electromagnetic Design of β_g= 0.9, 650 MHz Superconducting Radiofrequency Cavity

We present the electromagnetic design study of a multi cell, β_g= 0.9, 650 MHz elliptic superconducting radiofrequency cavity, which can be used for accelerating H- particles in the linear accelerator part of a Spallation Neutron source. The design has been optimized for maximum achievable acceleration gradient by varying the geometry parameters of the cavity, for which a simple and general procedure is evolved that we describe in the paper. For the optimized geometry, we have studied the higher order modes supported by the cavity, and the threshold current for the excitation of the regenerative beam break up instability due to dipole modes has been estimated. Lorentz force detuning studies have also been performed for the optimized design and the calculations are presented to find the optimum location of the stiffener ring to compensate for the Lorentz force detuning.

physics.acc-ph↗