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.

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.

Electron heat across the measurement

Retained laser-on and laser-off pixels

Inspect spectrum

How the measurements determine heat

The spectral shape constrains electron temperature; absolute scattering yield, finite geometry and the supplied profile family constrain density. The laser-off gate samples the adjacent background. Electron heat follows from their volume integral. Ion-inclusive heat requires the supplied equal-temperature closure.

The reported standard uncertainties use joint first-order propagation, declared plug-in shot/read variances and shared calibration across frames. The small readouts show relative standard uncertainty; tables retain absolute values. They are not confidence limits. Fit compatibility uses a conservative conditional moment check and reports no exact p-value. Counter rounding has a separate deterministic sensitivity; numerical spectrum bounds remain separate. Clock standards and the UTC receiver are simulated within this record.

The simulation programme uses UTC 2026-11-13 00:00:00.123456789 as provenance; only independent duration and receiver observations calibrate the clock.

The supplied low-speed noncollective spectrum includes finite aperture, known bulk drift and instrument broadening. A high-temperature relativistic spectrum and arbitrary-profile tomography lie outside this family.

Energy input and material terminals

Electrical supply loss and reflected RF are separate from deposited auxiliary heat. Wall calorimetry already includes radiation that misses the bolometer. Adding wall, divertor and absorbed bolometer energy counts each material loss once. Signed noisy residuals remain signed.

Confinement ratios use finite measured gates and the supplied ion closure. They are not a fitted instantaneous loss coefficient.

Gate	Start	Stop	Deposited heat	Material loss	Conditional heat change	Residual	Conditional finite-gate energy confinement	Conditional finite-gate conductive confinement

Gate	Electrical input	Forward RF	Reflected RF	Wall	Divertor	Bolometer

Magnetic reference and display scales

All hardware lengths use one uniform scale in a right-handed SI frame with Z upward. Gold handles are enlarged for picking; the enlarged marker follows the supplied field direction and is not a particle orbit. The finite coil paths, laser chord, receiver disk, bolometer aperture and opaque inner backstop use source-model geometry; coil conductor thickness is schematic.

Current opposes the supplied magnetic field in this cold force-free reference. The central solenoid carries zero capture-window current. The closed surfaces support no X-point or open SOL interpretation; the divertor targets are supplied heat-loss terminals. A static flux-correction bound admits only passive heating and does not establish stability.

Any fusion-power reference is externally supplied and separate from this plasma model. The experiment reports no calculated fusion gain, ITER performance or net electrical output.

ITER components Fixed-boundary equilibrium benchmark Thomson scattering, ITER International School

Retained frames and raw pixels

Frame	Elapsed time	Peak electron density	Axis electron temperature	Electron heat	Total heat with equal ion temperature	Support

Pixel	Laser on	Laser off	Used in reconstruction

Independent references and shared covariance

Pixel	Quantum efficiency	Independent spectral coverage

Rows and columns are retained frame indices. Blank cells are unsupported. This matrix comes from the selected record and retains shared metrology; it does not pool separate captures.

Forward reference for this local capture

These generating references are separate from measured heat and never enter the raw-only reconstruction. Imported measurements have no reconstructed generating truth.

Save and reopen measurements

Saved record

Import complete measurement history

Exports preserve complete raw references, readouts, units, identity and selection. A valid archive replaces this session only after checking and reconstruction. Generating answers are not archived.

Open an empty session

Read how magnetic confinement, heating and diagnostics connect

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 misconceptionClosed magnetic surfaces prove that a plasma is stable.

Better mental modelThey 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 misconceptionElectron temperature gives a direct measurement of all plasma heat.

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

Run the experiment

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.
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.
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.
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.
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.

Tokamak Magnetic Confinement and Heat Measurement

Magnetic surfaces and measured plasma heat

Core mathematical model

Toroidal and poloidal magnetic field

Heating and losses change thermal energy

Electron temperature broadens scattered light

Electron heat and conditional total heat

Common difficulties

Do closed surfaces establish stability?

Does the laser measure ion heat?

Run the experiment

Inspect the winding field

Compare heating and cooling

Distinguish heat-loss channels

Move the laser off axis

Check reference coverage

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