---
title: "Tokamak Magnetic Confinement and Heat Measurement Interactive Lab | Sandbox Physics"
description: "How does a magnetic field contain plasma, and how can an experiment measure its heat?"
canonical_url: "https://sandboxphysics.com/labs/tokamak-iter/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/tokamak-iter/"
last_modified: "2026-11-14"
---

# Tokamak Magnetic Confinement and Heat Measurement

**How does a magnetic field contain plasma, and how can an experiment measure its heat?** Toroidal and poloidal magnetic fields combine into twisting field lines on magnetic surfaces. Electron scattering broadens the laser spectrum as temperature rises. Independent calibration and supplied density and temperature profiles connect that spectrum to electron thermal energy, which can be compared with heating input and cooling losses.

Follow closed magnetic surfaces and move a laser chord across the plasma. Compare electron scattering spectra, heating input and material energy losses as the electrons heat and cool.

> Interactive simulation: open this page in a web browser to change the parameters and run the model.

## Follow the field, measure the heat

Electrical input $400\,\mathrm{kW}$ Conductive confinement time $60\,\mathrm{ms}$ Radiation rate $5\,\mathrm{s}^{-1}$ Thomson chord offset $0\,\mathrm{m}$ Magnetic scale $1$

Prescribed axis field: $5\,\mathrm{T}$

A capture follows thermal evolution with paired laser-off readings and independent references.

Shape and supplied assumptions

Elongation $1.2$

Ampere-turns per reference winding: $4.06\times10^6\,\mathrm{A\,turn}$

Density and temperature have supplied flux-surface profiles. Ion-inclusive heat assumes equal ion and electron temperatures. The magnetic geometry remains the cold force-free reference during heating.

Inspect the magnetic geometry, then acquire a spectrum.

Model assumptions

This low-temperature, low-pressure teaching apparatus borrows ITER component roles with separately supplied dimensions and parameters. A fixed-boundary cold force-free magnetic reference has an ideally held current. Eighteen finite toroidal windings approximate a continuous winding; the central solenoid has zero current during capture. Heat is a passive perturbation with a static flux-correction bound, which does not establish stability. Closed surfaces have no X-point or open scrape-off layer; divertor targets receive a supplied thermal partition. Classical noncollective low-speed Doppler scattering integrates finite beam, chord, receiver and pixels. Independent finite references and paired laser-off readouts support reconstruction. Density, temperature and emissivity use supplied profile families; ion temperature equal to electron temperature is an external closure. Transport, radiation rates and energy partitions are teaching inputs. The apparatus does not establish arbitrary-profile tomography, ITER performance, a self-consistent hot equilibrium, transient MHD, fusion gain or net electricity. Any supplied fusion-power reference remains separate from calculated plasma heating. Expired or inadequate references retain raw readouts.

[Read how magnetic confinement, heating and diagnostics connect](https://sandboxphysics.com/stories/instruments/tokamak-iter/)

## Magnetic surfaces and measured plasma heat

**Background** Charged particles gyrate around magnetic field lines. A tokamak combines toroidal and poloidal fields so the lines wind around a torus on magnetic surfaces.

**Why it matters** Magnetic confinement and heating have different jobs. Scattered laser light probes electron motion; material terminals record where heat leaves the plasma.

- **Focus question**: How can magnetic geometry be connected to measured electron heat?
- **One-sentence intuition**: Magnetic surfaces describe the supplied field; calibrated scattering spectra determine electron temperature, density and heat.

### Core mathematical model

#### Toroidal and poloidal magnetic field

$$
\mathbf B=\frac{\nabla\psi\times\mathbf e_\phi+F(\psi)\mathbf e_\phi}{R}
$$

The flux function gives the poloidal field and a second function gives the toroidal field. This apparatus holds a supplied cold fixed boundary and admits only a passive thermal perturbation.

#### Heating and losses change thermal energy

$$
\frac{dW}{dt}=P_{\mathrm{aux}}+P_{\alpha,\mathrm{supplied}}-\left(\tau_{\mathrm{cond}}^{-1}+\lambda_{\mathrm{rad}}\right)W
$$

Conduction and radiation remove heat. Their coefficients are supplied inputs; the measurement still reconstructs changing heat and terminal energies from independent readouts.

#### Electron temperature broadens scattered light

$$
x=\frac{\omega_s-\omega_0}{\omega_0},\qquad\sigma_x^2=|\mathbf n_s-\mathbf n_i|^2\frac{eT_e}{m_ec^2}
$$

Electron temperature is expressed in electronvolts. Known mean drift is included separately from random motion. Finite aperture, spatial profiles and spectrometer broadening are integrated before pixel binning.

#### Electron heat and conditional total heat

$$
W_e=\frac32e\int n_eT_e\,dV,\qquad W=2W_e\quad\text{only if }T_i=T_e
$$

Thomson scattering diagnoses electrons. Ion heat needs another measurement or a supplied closure. Doubling electron heat here assumes equal ion and electron temperatures.

### Common difficulties

#### Do closed surfaces establish stability?

**Typical misconception** Closed magnetic surfaces prove that a plasma is stable.

**Better mental model** They describe the supplied field geometry. Stability requires perturbation dynamics; a static flux-correction bound does not determine those dynamics.

#### Does the laser measure ion heat?

**Typical misconception** Electron temperature gives a direct measurement of all plasma heat.

**Better mental model** Thomson scattering diagnoses electrons. The displayed ion-inclusive heat requires the supplied equal-temperature closure.

### Run the experiment

1. 01

   #### Inspect the winding field

   Choose the magnetic view and adjust Magnetic scale and Elongation.

   **What to observe:** The same flux function generates the surfaces. Heating leaves this supplied cold reference geometry fixed.

2. 02

   #### Compare heating and cooling

   Choose Heating pulse, then Free cooling. Inspect electron heat over time.

   **What to observe:** Input competes with losses during heating. Conduction and radiation continue after the input stops.

3. 03

   #### Distinguish heat-loss channels

   Compare Stronger radiation and Faster conductive loss, then expand the terminal measurements.

   **What to observe:** Both can accelerate cooling. Bolometric, wall and divertor readings distinguish how energy leaves.

4. 04

   #### Move the laser off axis

   Choose Off-axis chord or drag the laser-chord handle. Compare the laser-on and laser-off pixels.

   **What to observe:** Finite beam and receiver areas select a spatial mixture. Profile and absolute references support reconstruction; brightness alone cannot determine temperature.

5. 05

   #### Check reference coverage

   Choose Late reference and compare early and late readouts.

   **What to observe:** Pixels outside reference coverage remain available. Dependent temperature and heat estimates are withheld.

Physical conclusion

Field geometry, electron diagnostics and heat-flow measurements answer complementary physical questions.

## Related experiments and articles

How physics instruments measure · Reading path

### How physics instruments measure

Articles on this path that use this experiment, followed by the other experiments they suggest.

1. [Article **How a tokamak holds heat and measures where it goes**](https://sandboxphysics.com/stories/instruments/tokamak-iter/)

Fields & matter · Starter path

## From a field to an electron microscope

Map an electric field and steer a charged particle. Then find the electron's wavelength and use electron beams to see a crystal and a surface.

[Start here → **Make an Electric Field Visible** Move the probe around a dipole and check that the field always points downhill on the potential landscape. Observe · 8 min](https://sandboxphysics.com/labs/electric-field/)

1. [1 Make an Electric Field Visible](https://sandboxphysics.com/labs/electric-field/)
2. [2 A Charge Bending through Fields](https://sandboxphysics.com/labs/charged-particle/)
3. [3 Electron Wavelength & Voltage](https://sandboxphysics.com/labs/electron-wavelength/)
4. [4 Electron Diffraction & Reciprocal Space](https://sandboxphysics.com/labs/electron-diffraction/)
5. [5 TEM Bright Field, Dark Field & SAED](https://sandboxphysics.com/labs/tem-mode-selector/)
6. [6 SEM Secondary-Electron Topography](https://sandboxphysics.com/labs/sem-topography/)

[View the full path →](https://sandboxphysics.com/topics/fields-and-matter/#starter-path)