Stellarator/Helical Confinement

The stellarator is a magnetic confinement fusion device that confines plasma using only external magnetic coils. It was invented by Lyman Spitzer at Princeton University in 1951. The name combines “stellar” (relating to stars) and “generator.”

In Japan, a variant called the “helical device” has developed independently, with the Large Helical Device (LHD) leading the world.

Basic Principles

Differences from Tokamak

While a tokamak generates the poloidal field through plasma current, a stellarator forms the complete magnetic configuration using only external coils.

Feature	Tokamak	Stellarator
Poloidal field	Plasma current	External coils
Plasma current	Required	Not required
Operation mode	Pulsed (in principle)	Steady-state possible
Disruption	Possible	Does not occur
Coil geometry	Relatively simple	Complex

Rotational Transform

In stellarators, the geometric arrangement of coils generates a rotational transform $\iota$. The rotational transform represents the angle advanced in the poloidal direction while a field line goes once around toroidally:

$$\iota = \frac{2\pi}{\text{toroidal turns/poloidal turn}} = \frac{1}{q}$$

where $q$ is the safety factor.

Types of Magnetic Configurations

Classical Stellarator

The earliest design with a figure-8 twisted torus shape. No longer in use today.

Heliotron/Helical

A method using continuous helical coils. Japan’s Large Helical Device (LHD) uses this approach.

LHD employs helical coils with l = 2 and m = 10, where l is the poloidal period number and m is the toroidal period number.

Modular Stellarator

A method using complex three-dimensional modular coils. Wendelstein 7-X is the prime example of this approach. It achieves a magnetic configuration designed through computer optimization.

Confinement by External Coils

Coil Design Optimization

Stellarator coils have complex three-dimensional shapes. Design requires optimization of:

1. Maximizing particle confinement
2. Ensuring MHD stability
3. Minimizing heat and particle transport
4. Manufacturability

Quasi-symmetry

In modern stellarator design, the concept of “quasi-symmetry” is important. While perfect axisymmetry is impossible, effective symmetry for particle orbits minimizes neoclassical transport.

Types of quasi-symmetry include:

• Quasi-axisymmetry (QA)
• Quasi-helical symmetry (QH)
• Quasi-isodynamic (QI)

Wendelstein 7-X employs QI configuration, while HSX uses QH configuration.

Advantages of Steady-State Operation

The greatest advantage of stellarators is the inherent capability for steady-state operation.

Constraints of Tokamaks

In tokamaks, maintaining plasma current requires either:

1. Changing magnetic flux of the central solenoid (finite time)
2. External current drive (low efficiency)

This is a barrier to steady-state operation.

Superiority of Stellarators

In stellarators:

• No flux consumption since plasma current is not required
• Bootstrap current does not affect confinement
• Operation can continue with auxiliary heating alone

For power reactors, continuous operation offers significant advantages in terms of facility availability and economics.

Why No Disruptions

Tokamak disruptions occur due to rapid collapse of plasma current. In stellarators, since plasma current is not essential for confinement:

1. Current quench does not occur
2. Large electromagnetic forces are not generated
3. No runaway electron problem

This represents a major advantage in terms of safety and device lifetime.

Representative Devices

Wendelstein 7-X (W7-X)

The world’s largest stellarator, operated by the Max Planck Institute for Plasma Physics (IPP) in Germany.

Parameter	Value
Major radius	5.5 m
Minor radius	0.53 m
Magnetic field	3 T
Heating power	10 MW
Number of coils	50 (non-planar superconducting)

W7-X is a device to demonstrate the concept of optimized stellarators, and began operation in 2015. In 2022, it set a record for energy confinement time.

Major achievements:

• High energy confinement (exceeding ISS04 scaling)
• Multi-minute long-pulse discharges
• Demonstration of as-designed magnetic configuration

Large Helical Device (LHD)

The world’s largest helical device, operated by the National Institute for Fusion Science (NIFS) in Japan.

Parameter	Value
Major radius	3.9 m
Minor radius	0.65 m
Magnetic field	3 T (max 4 T)
Heating power	23 MW

LHD features:

• l = 2 helical configuration
• High-density plasma confinement research
• Long-pulse discharge (over 1 hour steady-state operation achieved)
• Fusion reaction research with deuterium experiments

LHD started deuterium experiments in 2017 and has obtained important data in both plasma physics and fusion engineering.

HSX (Helically Symmetric Experiment)

A quasi-helical symmetric stellarator at the University of Wisconsin, USA. Though a small device, it plays an important role in experimentally verifying quasi-symmetry physics.

Challenges and Current Status

Manufacturing Complexity

The three-dimensionally complex coil geometry presents challenges in both manufacturing cost and precision. For W7-X, the tolerance for coil position was set to sub-millimeter levels.

Confinement Performance

Historically, stellarator confinement performance has been inferior to tokamaks. However, this gap is narrowing with optimized designs.

Scaling

The stellarator energy confinement time scaling is represented by the ISS04 scaling:

$$\tau_E^{\text{ISS04}} = 0.134 \cdot a^{2.28} \cdot R^{0.64} \cdot P^{-0.61} \cdot \bar{n}_e^{0.54} \cdot B^{0.84} \cdot \iota^{0.41}$$

where $a$ is the minor radius, $R$ is the major radius, $P$ is the heating power, $\bar{n}_e$ is the line-averaged electron density, $B$ is the magnetic field strength, and $\iota$ is the rotational transform.

Future Outlook

Potential as Power Reactor

Stellarators are attractive as power reactors due to steady-state operation and absence of disruptions. However, further improvement in confinement performance and reduction in manufacturing costs are needed.

HELIAS

In Europe, a power reactor conceptual design HELIAS (Helical Advanced Stellarator) is being considered based on W7-X results.

Compact Stellarators

With high-temperature superconductors and advanced manufacturing technologies, more compact stellarators are expected to become feasible.

Related Topics

• Confinement Methods: Overview - Overview of confinement methods
• Tokamak Confinement - Alternative method using plasma current
• Glossary: Stellarator - Basic definition
• Glossary: Confinement - Concept of confinement