Exploring Electric Fields in IEC Fusion Reactors
Our electric field visualizer computes and visualizes the electric field generated by different configurations of cathode rings in inertial electrostatic confinement (IEC) fusion reactors.
IEC fusion devices use electric fields to confine plasma, facilitating nuclear fusion reactions. Understanding the electric field distribution within these devices is crucial for optimizing performance and efficiency.
The electric potential \( V \) within the reactor is computed by solving the Laplace equation:
$$ \nabla^2 V = 0 $$
We employ the finite difference method (FDM) to discretize the Laplace equation on a 3D grid. The update rule for the potential at each grid point \( (i, j, k) \) is given by:
$$ V_{i,j,k} = \frac{1}{6} \left( V_{i+1,j,k} + V_{i-1,j,k} + V_{i,j+1,k} + V_{i,j-1,k} + V_{i,j,k+1} + V_{i,j,k-1} \right) $$
This iterative method updates the potential until convergence is achieved based on a specified tolerance.
The electric field \( \mathbf{E} \) is calculated from the potential using the negative gradient:
$$ \mathbf{E} = -\nabla V $$
We generate cross-sectional slices of the electric field magnitude and overlay field lines to visualize the directionality. The simulations are performed at various angles \( \alpha \) and \( \beta \), and heights to provide comprehensive insights.
Explore the electric field distributions for various cathode configurations. Each configuration below features a row of three simulations at different angles.
Computation grid size: \(400 \cdot 400 \cdot 400\)
Iterations until convergence: \( 212,151 \)
Final delta: \( 9.9996 \cdot 10^{-5} \)
Computation time: \( 30,294.67 \) seconds
GPU: Nvidia RTX 4080 Super
Computation grid size: \(400 \cdot 400 \cdot 400\)
Iterations until convergence: \( 186,066 \)
Final delta: \( 9.9999 \cdot 10^{-5} \)
Computation time: \( 39,051.54 \) seconds
GPU: Nvidia RTX 4080 Super
Computation grid size: \(400 \cdot 400 \cdot 400\)
Iterations until convergence: \( 164,913 \)
Final delta: \( 9.9995 \cdot 10^{-5} \)
Computation time: \( 45,804.51 \) seconds
GPU: Nvidia RTX 4080 Super
Computation grid size: \(400 \cdot 400 \cdot 400\)
Iterations until convergence: \( 126,423 \)
Final delta: \( 9.9999 \cdot 10^{-5} \)
Computation time: \( 38,541.29 \) seconds
GPU: Nvidia A100
Future enhancements include incorporating dynamic plasma behavior, ion trajectories, and integrating real-time simulation capabilities. This program is already very computationally demanding without accounting for plasma dynamics, so increasing complexity may not be feasable on the current available hardware. The electric field data is likely a good appromixation, so using it in particle-in-cell simulations may provide valuable insights into how cathode geometries influence ion tragetories within IEC fusion reactors.
Visit our GitHub repository for source code and more information.