Computational Modeling of Multi-Scale Plasma Flow and Magnetic Flux Dynamics in Tokamak System Using Matlab
Author : Waqas Javaid
Abstract
A reduced magnetohydrodynamic numerical model is presented to investigate plasma flow behavior and magnetic flux evolution in a tokamak configuration. The study employs a two-dimensional polar grid to simulate the coupled dynamics of magnetic flux, pressure, and safety factor under magnetically confined conditions. Time-dependent diffusion equations are used to capture the evolution of poloidal flux and plasma pressure, while simplified velocity and magnetic field structures represent plasma flow effects [1]. Key plasma performance metrics, including magnetic flux RMS, energy evolution, safety factor distribution, and plasma beta, are analyzed. The results demonstrate smooth flux diffusion, stable pressure decay, and coherent safety factor evolution over time. Mode spectrum analysis reveals dominant low-order magnetic structures governing plasma behavior [2]. Energy normalization confirms numerical stability throughout the simulation. The proposed framework provides an efficient tool for multi-scale analysis of tokamak plasma dynamics and offers insights for flow optimization and magnetic stability studies [3].
Introduction
Magnetic confinement fusion in tokamak devices relies on the controlled interaction between plasma flow, magnetic fields, and pressure gradients to achieve stable and efficient operation [4]. Understanding the evolution of magnetic flux and plasma flow structures is therefore essential for improving confinement performance and mitigating instabilities.
Due to the extreme physical conditions inside tokamaks, numerical modeling has become a primary tool for investigating plasma behavior across multiple spatial and temporal scales. Reduced magnetohydrodynamic (MHD) models provide a computationally efficient framework that captures the dominant physics governing plasma dynamics while avoiding the complexity of full kinetic descriptions [5]. In this context, the safety factor profile plays a critical role in determining magnetic stability and transport characteristics.
Table 1: Initial Plasma Profiles
Quantity | Expression / Profile | Notes |
Poloidal flux | Ψ = (1 – (R/a)²)² | Axisymmetric profile |
Pressure | p = (1 – (R/a)²)³ | Maximum at core |
Safety factor | q(r) = 1 + 2.5 (r/a)² | Increases from core to edge |
Radial velocity | V_R = 0.01 sin(3θ) sin(πR/a) | Weak poloidal flow |
Angular velocity | V_θ = 0.01 cos(3θ) sin(πR/a) | Poloidal component |
Plasma pressure and magnetic flux diffusion strongly influence energy confinement and beta limits in magnetically confined systems. Recent advances in computational resources have enabled detailed parametric studies of tokamak plasmas using simplified geometries. Such studies are particularly valuable for exploring optimization strategies and sensitivity to key physical parameters. Moreover, multi-scale numerical approaches are increasingly relevant for nano- and micro-scale plasma modeling applications, where localized transport and flow effects become significant [6]. This work presents a two-dimensional numerical investigation of plasma flow, magnetic flux evolution, and energy dynamics in a tokamak geometry using a reduced MHD framework. The proposed model aims to provide physical insight into coupled plasma–magnetic interactions while maintaining numerical stability and computational efficiency.
1.1 Background and Motivation
Magnetic confinement fusion represents one of the most promising pathways toward sustainable and clean energy production, with tokamak devices being the most extensively studied configuration. In a tokamak, plasma is confined by strong toroidal and poloidal magnetic fields that must be carefully controlled to maintain stability [7]. Plasma flow, pressure gradients, and magnetic flux evolution are deeply interconnected and directly influence confinement quality. Experimental investigation of these interactions is extremely challenging due to high temperatures and limited diagnostic access. Consequently, numerical modeling has become an indispensable tool for understanding tokamak plasma behavior. Simplified computational frameworks allow researchers to isolate key physical mechanisms governing stability and transport. In particular, reduced magnetohydrodynamic models capture essential plasma dynamics while remaining computationally tractable [8]. These models are well suited for parametric studies and conceptual optimization of plasma operating conditions. Understanding these fundamental interactions is essential for advancing tokamak design and control strategies.
1.2 Role of Numerical and Multi-Scale Modeling
Plasma behavior in tokamak systems spans a wide range of spatial and temporal scales, from microscopic transport processes to macroscopic magnetic structures. Full kinetic simulations that resolve all scales are often computationally prohibitive for routine analysis. Reduced MHD approaches provide an effective compromise by focusing on dominant large-scale phenomena while incorporating the influence of smaller-scale effects through simplified terms. Such models enable systematic exploration of magnetic flux diffusion, pressure evolution, and flow-induced transport [9]. Multi-scale numerical modeling is particularly relevant for nano- and micro-scale plasma studies, where localized gradients can significantly affect global behavior. Advances in computational techniques have further enhanced the accuracy and stability of reduced models. These developments have broadened their application to optimization and control-oriented studies. As a result, reduced MHD simulations have become a cornerstone of theoretical and computational fusion research. They also serve as a bridge between analytical theory and experimental observation.
1.3 Objectives and Scope of the Present Study
The primary objective of this study is to numerically investigate plasma flow dynamics and magnetic flux evolution in a tokamak configuration using a reduced MHD framework. A two-dimensional polar grid is employed to represent the cross-sectional geometry of the tokamak plasma [10]. Time-dependent diffusion equations are used to model the evolution of magnetic flux and plasma pressure. The safety factor profile is incorporated to assess magnetic stability and its temporal variation. Key plasma performance metrics, including energy evolution, plasma beta, and mode spectra, are systematically analyzed. The model emphasizes numerical stability and clarity of physical interpretation rather than exhaustive physical complexity. Through this approach, the study aims to provide insight into plasma flow optimization and magnetic confinement behavior. The results contribute to a deeper understanding of coupled plasma–magnetic interactions in tokamak systems and support future extensions toward control and optimization studies.
1.4 Significance of Plasma Flow and Magnetic Stability
Plasma flow plays a crucial role in regulating transport processes and stabilizing magnetohydrodynamic instabilities in tokamak devices. Sheared flows can suppress turbulence and enhance energy confinement, thereby improving overall plasma performance. The interaction between plasma flow and magnetic field structures strongly influences the evolution of magnetic flux surfaces. Variations in pressure and flow profiles can modify the safety factor, which is a key indicator of magnetic stability. Accurate modeling of these effects is essential for predicting stable operating regimes [11]. Reduced MHD models provide a practical framework for examining such interactions without excessive computational cost. By capturing the dominant flow–field coupling, these models help identify trends relevant to confinement optimization. Understanding flow-induced stabilization mechanisms is particularly important for next-generation tokamak designs. This motivates the inclusion of simplified velocity fields in the present numerical study.
1.5 Computational Framework and Model Assumptions
The numerical framework adopted in this work is designed to balance physical realism with computational efficiency. A two-dimensional axisymmetric representation is used to describe the tokamak cross-section, assuming toroidal symmetry. Magnetic flux and pressure evolution are governed by diffusion-type equations that approximate resistive and transport effects. Prescribed magnetic and velocity field structures are introduced to emulate plasma flow behavior. While kinetic effects and full nonlinear MHD dynamics are not explicitly resolved, the model retains the essential features required for qualitative analysis [12]. Such assumptions are common in early-stage design studies and parametric investigations. The discretization strategy ensures numerical stability and smooth temporal evolution [13]. This approach enables efficient exploration of plasma response under varying conditions. The simplified framework also allows clear interpretation of the resulting physical trends.
1.6 Relevance to Nano-Scale and Future Applications
Although tokamak plasmas are macroscopic systems, the underlying transport and stability mechanisms are influenced by processes occurring at smaller spatial scales. Multi-scale numerical modeling provides a bridge between nano-scale transport phenomena and global plasma behavior [14]. The present study contributes to this perspective by offering a computationally efficient platform for examining scale interactions. Such models are increasingly relevant in nano-structured materials used in plasma-facing components and diagnostic systems. Insights gained from simplified tokamak simulations can inform the design of advanced confinement concepts and control algorithms. Furthermore, reduced MHD models serve as a foundation for incorporating additional physics, such as turbulence models or active control strategies. The results presented here therefore have broader relevance beyond the immediate tokamak configuration [15]. They support ongoing efforts toward optimized, stable, and efficient magnetic confinement systems.
Problem Statement
Despite significant progress in tokamak research, accurately predicting the coupled evolution of plasma flow, magnetic flux, and pressure remains a challenging problem due to the nonlinear and multi-scale nature of magnetically confined plasmas. Experimental investigation of these interactions is limited by extreme operating conditions and restricted diagnostic access. High-fidelity kinetic and full MHD simulations, while accurate, are computationally expensive and impractical for rapid parametric analysis. As a result, there is a need for simplified yet stable numerical frameworks that can capture the dominant plasma–magnetic interactions. In particular, understanding how magnetic flux diffusion, pressure evolution, and safety factor variations influence plasma stability is critical. Existing reduced models often focus on isolated effects and lack integrated analysis of flow, energy, and stability metrics. This limits their usefulness for optimization-oriented studies. Therefore, a computationally efficient reduced MHD model is required to systematically analyze plasma flow dynamics, magnetic flux evolution, and energy behavior in tokamak configurations while maintaining numerical robustness and physical interpretability.
Mathematical Approach
The mathematical approach in this study is based on a reduced magnetohydrodynamic (MHD) framework that captures the essential dynamics of tokamak plasma while remaining computationally efficient. The plasma is modeled in a two-dimensional axisymmetric polar coordinate system, representing the cross-section of the toroidal device. The evolution of the poloidal magnetic flux, (Psi), is described by a diffusion-type equation that approximates resistive magnetic diffusion and large-scale flux redistribution. Similarly, the plasma pressure, (p), is modeled using a diffusion equation to account for transport effects and energy redistribution. The safety factor, (q(r)), is introduced as a function of the radial coordinate to quantify the magnetic shear and assess stability. Magnetic field components in the poloidal plane are expressed in terms of (Psi), while prescribed velocity fields represent simplified plasma flow structures. Temporal evolution is achieved using an explicit time-stepping scheme, with small time increments ensuring numerical stability. Spatial derivatives are approximated using finite difference methods on a uniform polar grid. Key performance metrics, such as magnetic flux RMS, energy, and plasma beta, are computed at each time step to quantify global plasma behavior. Fourier analysis is employed to examine the mode spectrum of the magnetic flux, identifying dominant structures that govern plasma dynamics. Contour and surface plots are generated to visualize pressure, flux, and velocity fields across the poloidal plane. The model assumes toroidal symmetry and neglects full kinetic effects, focusing instead on capturing large-scale flow–field interactions. Nonlinear coupling between pressure and magnetic flux is partially represented through the time-dependent evolution of the governing equations. The overall framework balances physical fidelity and computational tractability, allowing systematic parametric studies. Boundary conditions are applied at the plasma edge to maintain confinement consistency. Normalization of energy and flux ensures stability of numerical results. This mathematical approach provides a foundation for exploring plasma flow optimization, magnetic stability, and multi-scale transport phenomena in tokamak systems. The reduced magnetohydrodynamic (MHD) model used in this study describes the evolution of the tokamak plasma through coupled equations for magnetic flux, plasma pressure, and velocity. The poloidal magnetic flux:
The poloidal magnetic flux evolves according to a diffusion-like equation:
The effective magnetic diffusivity and Laplacian operator in polar coordinates.The plasma pressure is:
The plasma pressure is modeled using a similar diffusion equation:
The plasma flow is introduced through a simplified poloidal velocity field which interacts with the magnetic field to modify transport and flux evolution. The velocity field satisfies a prescribed profile:
The maximum velocity amplitude is the mode number and minor radius of the tokamak. The safety factor is included to quantify the magnetic shear and is defined as a radially varying function where constants are determined from equilibrium considerations.
The numerical implementation uses a uniform polar grid with angular points. Finite difference approximations are applied to spatial derivatives, while explicit time-stepping ensures temporal evolution. Key plasma metrics, including the root-mean-square magnetic flux, normalized energy, and plasma beta, are computed at each time step to assess global behavior. Fourier analysis of the poloidal flux along the midplane provides insight into dominant mode structures. Boundary conditions at the plasma edge are set to maintain confinement consistency. The velocity and magnetic field coupling allows the study of flow-driven stabilization effects. The simplified framework neglects full kinetic and three-dimensional nonlinear effects but captures the essential physics of magnetic diffusion, pressure redistribution, and flow interaction. Contour, quiver, and surface plots visualize the spatial evolution of flux, pressure, and velocity. Normalization of energy and flux ensures numerical stability. Overall, this mathematical approach provides a computationally efficient yet physically meaningful platform to study plasma flow optimization, magnetic stability, and transport phenomena in tokamak configurations.
Methodology
The present study employs a computational methodology based on a reduced magnetohydrodynamic (MHD) framework to investigate plasma flow and magnetic flux evolution in a tokamak configuration [16]. A two-dimensional polar grid is used to represent the cross-sectional plane of the toroidal plasma, with discretization along the radial and angular directions. Initial profiles for magnetic flux, plasma pressure, and safety factor are prescribed based on equilibrium conditions, while simplified poloidal velocity fields are imposed to emulate plasma flow.
Table 2: Key Metrics at Final Time Step
Metric | Symbol | Value | Notes |
RMS Magnetic Flux | Ψ_rms | 0.70 | Normalized |
Total Plasma Energy | E | 1.01 | Normalized |
Plasma Beta | β | 0.0303 | – |
Safety Factor (Center) | q_core | 1.00 | Radial center |
Safety Factor (Edge) | q_edge | 3.50 | Plasma edge |
Dominant Mode Number | n | 1 | From FFT analysis |
Time evolution of the system is computed using explicit finite difference schemes for the diffusion-like equations governing flux and pressure. Small time increments are chosen to ensure numerical stability and accurate capture of transient dynamics. Magnetic field components are derived from the poloidal flux, and the safety factor profile is updated at each time step to reflect evolving magnetic shear [17]. Key plasma metrics, including magnetic flux RMS, energy, and plasma beta, are calculated iteratively to quantify global behavior. Fourier analysis of the midplane flux is performed to identify dominant mode structures and assess stability characteristics. Visualization of results is carried out using contour plots for pressure and flux, quiver plots for velocity and magnetic field vectors, and surface plots for three-dimensional flux representation. Boundary conditions are applied at the plasma edge to maintain confinement consistency and prevent unphysical diffusion. The methodology also includes normalization of energy and flux to track numerical stability throughout the simulation. By combining these steps, the approach allows systematic evaluation of plasma flow effects on magnetic flux evolution, energy dynamics, and stability metrics [18]. The framework is computationally efficient, enabling parametric studies and analysis of flow-induced optimization strategies. This methodology provides a structured and physically meaningful platform for studying multi-scale interactions in tokamak plasmas, with potential extensions to control and optimization applications in future research [19].
Design Matlab Simulation and Analysis
The simulation presented in this study models plasma flow and magnetic flux evolution in a tokamak using a reduced magnetohydrodynamic framework.
Table 3: Simulation Parameters
Parameter | Symbol | Value | Units |
Major radius | R0 | 2.0 | m |
Minor radius | a | 0.5 | m |
Toroidal field | B0 | 3.0 | T |
Magnetic permeability | μ0 | 4π × 10⁻⁷ | H/m |
Initial plasma beta | β0 | 0.03 | – |
Radial grid points | Nr | 50 | – |
Angular grid points | Nθ | 60 | – |
Time step | dt | 1 × 10⁻⁷ | s |
Number of time steps | Nt | 10 | – |
The tokamak cross-section is discretized on a two-dimensional polar grid with radial and angular points to capture the spatial variation of plasma parameters. Initial conditions for magnetic flux, plasma pressure, and safety factor are prescribed based on equilibrium-like profiles, while simplified poloidal velocity fields represent plasma flow effects. Magnetic field components are derived from the poloidal flux, providing a consistent representation of the in-plane field. Time evolution is performed using explicit finite-difference schemes for the diffusion-like equations governing flux and pressure, with small time steps ensuring numerical stability. At each time step, the safety factor profile is updated to reflect evolving magnetic shear. Key plasma metrics, including magnetic flux RMS, total energy, and plasma beta, are computed to quantify global behavior and assess stability. Fourier analysis of the poloidal flux along the midplane identifies dominant mode structures, providing insight into plasma dynamics. Contour plots are used to visualize the spatial distribution of pressure and flux, while quiver plots illustrate the velocity and magnetic field vectors. Surface plots present three-dimensional representations of flux surfaces for enhanced visualization. The evolution of energy and beta is normalized and tracked to monitor numerical consistency. Radial profiles of flux and pressure reveal how these parameters vary across the tokamak minor radius. The simulation captures smooth diffusion of magnetic flux, coherent pressure redistribution, and gradual changes in the safety factor. Mode spectrum analysis highlights the influence of low-order structures on overall plasma behavior. The framework is computationally efficient, allowing multiple parametric studies within reasonable runtime. Boundary conditions at the plasma edge maintain confinement consistency and prevent unphysical effects. Overall, the simulation provides a comprehensive picture of the coupled evolution of flow, flux, and pressure in a tokamak plasma, offering insights for flow optimization, magnetic stability analysis, and future control-oriented studies.
Above figure presents the initial configuration of the poloidal magnetic flux (Psi) across the tokamak plasma cross-section. The flux is highest at the magnetic axis and decreases smoothly towards the edge, following the prescribed ((1-(R/a)^2)^2) profile. This distribution ensures a physically consistent magnetic equilibrium for subsequent evolution. The radial variation illustrates the concentration of magnetic energy near the center, while the angular uniformity reflects axisymmetric initialization. The image uses a color map to enhance visual clarity of flux gradients. Early flux structures establish the framework for plasma flow interactions and safety factor evolution. These initial conditions are critical for analyzing diffusion and transport processes. The smoothness of the flux also minimizes numerical artifacts in the simulation. Overall, this figure sets the baseline for understanding how the magnetic field evolves over time under resistive and flow effects.
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Above figure shows the spatial distribution of the plasma pressure (p) at the start of the simulation. The pressure is maximal at the center and decreases toward the plasma boundary, following a cubic profile ((1-(R/a)^2)^3). Contour levels provide a detailed visualization of pressure gradients, which drive plasma dynamics through their coupling with magnetic flux. High-pressure regions correspond to stronger confinement and indicate where flow-induced stabilization may be most effective. The smooth pressure profile minimizes artificial instabilities in the numerical solution. This distribution also influences energy evolution and beta values as the plasma evolves. The figure highlights the axisymmetric nature of the initial state, supporting a controlled study of radial diffusion. By comparing with later time steps, changes in pressure can be linked to transport and magnetic interactions.
Above figure illustrates the poloidal magnetic field using quiver vectors in the tokamak plane. The field is calculated from the derivatives of the poloidal flux (Psi). Vectors are longer near the central axis and decrease towards the edge, representing the spatial variation of field strength. This figure provides insight into the direction and magnitude of magnetic forces acting on plasma elements. The orientation of vectors reflects the expected poloidal rotation and magnetic shear. Sparse sampling is applied for clarity, showing overall field topology without clutter. This visualization helps understand how plasma flow interacts with magnetic structures. It also serves as a reference for comparing the impact of flux evolution on the field configuration. Observing the initial vectors is essential for interpreting later changes due to diffusion and flow.
Above figure plots the initial safety factor (q) as a function of normalized radius. The profile increases from the center to the edge, consistent with tokamak equilibrium design. The safety factor indicates the magnetic field line pitch and is critical for assessing stability against MHD instabilities. Low (q) values at the core suggest stronger magnetic shear, while higher values at the edge correspond to weaker confinement. This radial profile provides a baseline for evaluating the temporal evolution of (q). Understanding this distribution is essential for interpreting plasma stability and transport phenomena. The figure helps link the flux and pressure profiles to expected magnetic stability behavior.
Above figure shows how the RMS magnetic flux evolves over time due to diffusion and plasma flow effects. The gradual change indicates a smooth redistribution of magnetic energy in the plasma. The trend confirms numerical stability of the simulation. Fluctuations are minimal, consistent with the small time steps used in the model. This evolution provides insight into the global magnetic behavior rather than localized structures. It helps identify timescales over which significant flux changes occur. The RMS metric is useful for comparing different parametric cases. This figure links flux evolution to energy and beta trends.
Above figure presents the evolution of the safety factor as a function of time and normalized radius. The color map reveals small oscillations due to flux diffusion and the influence of plasma flow. Radial dependence is preserved, showing that core and edge regions respond differently. The safety factor evolution indicates potential changes in magnetic shear over time. This metric is critical for understanding stability and confinement quality. The visualization captures global trends rather than local fluctuations. The small variations highlight the stability of the initial configuration. It provides insight into how magnetic field topology adjusts dynamically.
Above figure displays the prescribed poloidal velocity field used in the simulation. The vectors illustrate radial and angular components of the flow across the tokamak plane. Flow amplitudes are small, consistent with weak plasma rotation. The pattern shows alternating directional regions due to the sinusoidal angular dependence. Velocity influences flux diffusion and stability through advection effects. Sparse quiver sampling ensures clarity. This figure helps interpret flow-driven modifications in flux and pressure distributions. The velocity structure provides a foundation for studying flow optimization strategies.
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Above figure presents the normalized energy evolution combining magnetic flux and pressure contributions. The smooth curve indicates numerical stability and energy conservation in the simulation. Energy increases or decreases slightly due to diffusion and flow interactions. This metric allows comparison of different simulation runs or parameter sets. Tracking energy trends is essential for understanding plasma confinement efficiency. The normalization ensures that results are dimensionless and comparable. The figure also serves as a consistency check for the model implementation.
Above figure shows how the plasma beta, representing the ratio of plasma pressure to magnetic pressure, evolves over time. Small oscillations arise due to the prescribed time-dependent variation. The beta evolution reflects changes in plasma confinement and pressure redistribution. Maintaining stable beta is important for avoiding MHD instabilities. The figure demonstrates that the simulation preserves physically reasonable pressure-to-magnetic pressure ratios. It provides insight into confinement quality under flow and diffusion effects.
Above figure presents the poloidal flux at the end of the simulation. Diffusion has smoothed sharp gradients, and the overall profile remains axisymmetric. Contour levels illustrate the spatial redistribution of magnetic flux over time. This final state can be compared to the initial configuration to evaluate flux transport efficiency. The figure highlights regions of high and low flux concentration. It also provides a visual reference for understanding mode structures in subsequent spectral analysis.
Above figure provides a 3D visualization of the poloidal flux surface, illustrating radial and angular variations in flux amplitude. Peaks correspond to the plasma core, while edges show reduced flux. The 3D perspective highlights both amplitude and topology of magnetic flux. Shading enhances smoothness and visual clarity. This plot is useful for interpreting flux evolution in combination with velocity and pressure effects. It also facilitates identification of localized structures that may influence stability.
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Above figure shows the amplitude of poloidal flux modes obtained via FFT along the midplane. Dominant low-order modes indicate large-scale magnetic structures governing plasma behavior. Higher-order modes are weaker due to smooth initial conditions and diffusion effects. The spectrum helps understand the spatial scales of magnetic features. It also serves as a diagnostic for mode growth or damping. This figure provides insight into potential resonances and stability characteristics.
Above figure presents the radial profiles of magnetic flux and plasma pressure along the tokamak midplane. Flux decreases smoothly from core to edge, while pressure exhibits a cubic decay, consistent with initial profiles. These profiles highlight radial transport and diffusion effects over time. Comparing radial variations provides insight into confinement and energy redistribution. The figure emphasizes the axisymmetric nature of the plasma and the smoothness of numerical solutions. Radial trends also relate to safety factor and beta variations. This visualization is essential for understanding coupled flux–pressure dynamics.
Results and Discussion
The simulation results demonstrate the coupled evolution of magnetic flux, plasma pressure, velocity fields, and safety factor in a tokamak cross-section [20]. The initial poloidal flux and pressure profiles provide smooth, axisymmetric baselines, which evolve under the influence of diffusion and weak poloidal flows. Magnetic flux RMS analysis shows gradual flux redistribution, confirming numerical stability and the effectiveness of the diffusion operator. Contour and surface plots reveal that the flux and pressure remain concentrated near the plasma core while gradually decreasing toward the edge, consistent with physical expectations. Velocity field visualization highlights alternating poloidal flow structures, which interact with the magnetic field to influence flux transport and stability [21]. Safety factor evolution indicates minor radial adjustments, suggesting that magnetic shear remains largely preserved during early-time dynamics. Energy evolution remains nearly constant when normalized, reflecting minimal numerical dissipation and stable plasma behavior. Plasma beta exhibits small oscillations due to the prescribed time-dependent variation, demonstrating the interplay between pressure and magnetic field. Fourier analysis of the midplane flux shows dominant low-order modes, confirming that large-scale structures govern the dynamics rather than high-frequency perturbations. Radial profiles of flux and pressure further emphasize smooth transport and diffusion effects [22]. The 3D flux surface visualization provides a comprehensive understanding of the spatial distribution of magnetic flux. Comparison of initial and final flux distributions shows that diffusion gradually reduces gradients while maintaining overall topology. The results indicate that the prescribed velocity fields can slightly modulate flux evolution without introducing instability. Safety factor trends suggest that the plasma configuration remains stable under the chosen parameters. Overall, the study confirms that reduced MHD modeling captures essential plasma–magnetic interactions efficiently. The simulation provides insights into energy confinement, flow-driven flux redistribution, and mode dynamics [23]. These results are valuable for understanding plasma stability, guiding optimization strategies, and informing future tokamak design and control studies.
Conclusion
This study presents a reduced magnetohydrodynamic simulation of plasma flow and magnetic flux evolution in a tokamak configuration. The results demonstrate smooth redistribution of poloidal flux and pressure, with dominant large-scale magnetic structures governing plasma behavior. Safety factor and plasma beta remain largely stable, indicating a numerically robust and physically consistent model [24]. Velocity fields slightly modulate flux evolution, highlighting the influence of flow on magnetic confinement. Energy normalization confirms minimal numerical dissipation and overall stability. Fourier analysis of the midplane flux reveals that low-order modes dominate the dynamics. Radial profiles emphasize coherent transport and diffusion effects from core to edge. The 3D flux visualization provides a clear understanding of spatial flux distribution. Overall, the reduced MHD framework efficiently captures essential plasma–magnetic interactions [25]. The study offers valuable insights for plasma flow optimization, stability assessment, and future tokamak design strategies.
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