Closed poloidal loops are a fundamental concept in magnetic confinement fusion, referring to magnetic field lines that form closed loops in the poloidal (toroidal minor radius) direction. In field-reversed configurations (FRCs) and other fusion devices, closed poloidal loops are essential for plasma confinement—they create a boundary between the confined plasma and the external region. Understanding closed poloidal loops is crucial for understanding how FRCs and similar configurations confine hot plasma.

Introduction

In magnetic confinement fusion, the goal is to contain hot plasma using magnetic fields. The topology of these magnetic fields—how the field lines are arranged—determines whether the plasma is confined or escapes. Closed poloidal loops represent one important type of magnetic field topology, particularly in field-reversed configurations.

Imagine a smoke ring: the magnetic field lines form closed loops that wrap around the plasma, creating a boundary. This is essentially what closed poloidal loops do in an FRC—they create a closed magnetic surface that contains the plasma. Unlike tokamaks, where field lines spiral around the torus, FRCs use field lines that close on themselves in the poloidal direction, creating a simpler but potentially less stable configuration.

Magnetic Field Topology

Poloidal vs. Toroidal

In toroidal fusion devices:

• Toroidal direction: Around the major axis (the donut hole)
• Poloidal direction: Around the minor axis (around the donut itself)
• Field lines: Can have components in both directions

Closed Poloidal Loops

Closed poloidal loops are field lines that:

• Close on themselves: Form complete loops
• Poloidal plane: Lie primarily in the poloidal plane
• Confinement: Create closed magnetic surfaces
• Boundary: Define the separatrix between confined and unconfined regions

Role in Field-Reversed Configurations

FRC Structure

In an FRC, closed poloidal loops:

• Create separatrix: Boundary between closed and open field lines
• Confine plasma: Plasma is trapped inside closed loops
• Self-generated: Created by plasma currents
• Simpler topology: No central conductor needed

Comparison with Tokamaks

Tokamaks:

• Use helical field lines (toroidal + poloidal)
• Require central conductor
• More complex topology

FRCs:

• Use closed poloidal loops
• No central conductor
• Simpler topology
• Potentially more compact

Physics

Field Reversal

The "field-reversed" in FRC refers to:

• External field: Points in one direction
• Internal field: Reversed direction inside plasma
• Closed loops: Field lines close within the plasma
• Separatrix: Boundary where field reverses

Confinement

Closed poloidal loops provide confinement by:

• Trapping particles: Charged particles follow field lines
• Closed surfaces: Particles stay on closed surfaces
• No escape: Particles can't cross closed loops easily
• Stability: Loop topology affects stability

Stability Considerations

Advantages

Closed poloidal loops can provide:

• Simple topology: Easier to understand and model
• High beta: Can achieve high plasma pressure
• Compact design: No central conductor needed

Challenges

Closed poloidal loops face:

• Instabilities: Can be unstable to various modes
• Tilt instability: FRCs can tilt and disrupt
• Shift instability: Plasma can shift off-axis
• Complex dynamics: Stability is complex

Applications

Field-Reversed Configurations

Closed poloidal loops are essential for:

• FRC formation: Creating the FRC structure
• Confinement: Maintaining plasma confinement
• Stability: Understanding FRC stability

Other Configurations

Similar concepts apply to:

• Spheromaks: Another compact torus configuration
• Other FRC variants: Various FRC-like configurations

Research and Development

Understanding closed poloidal loops is important for:

• FRC research: Developing FRC fusion concepts
• Stability analysis: Predicting FRC behavior
• Optimization: Designing better FRC configurations