IndexHeat & EntropyHoodie

Tokamak Hoodie

NESTED, NEVER TOUCHING | Pixelated Physics

\[\Delta^*\psi = -\mu_0R^2\frac{dp}{d\psi} - F\frac{dF}{d\psi}\]
$59.99 USD
$59.99 USD
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A tokamak holds a plasma hotter than the core of the Sun inside a ring-shaped vacuum vessel, without letting it touch the walls. Nested magnetic flux surfaces of a Solov’ev equilibrium, an exact solution of the Grad–Shafranov equation for a tokamak plasma. Pixel-art unisex hoodie in black; equation, symbols and sources in the physics panel below.

Color
Size

Size guide S–5XL · inches

Shipping calculated at checkout by destinationMade to order, ships in 2–5 business days

Details

Size & fitS–5XL

Unisex Heavy Blend hoodie (Gildan 18500), classic fit.

SizeWidthLengthSleeve
S202733.5
M222834.5
L242935.5
XL263036.5
2XL283137.5
3XL303238.5
4XL323339.5
5XL343440.5

Measurements in inches. Width and length ±1 in, sleeve (from center back) ±0.75 in.

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Shipping calculated at checkout by destination.

Delivery times & where we ship

Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.

Full refund & replacement policy

The physics

A tokamak holds a plasma hotter than the core of the Sun inside a ring-shaped vacuum vessel, without letting it touch the walls.

Magnetic field lines wind around the ring and lie on nested surfaces of constant flux ψ. In equilibrium the plasma pressure is balanced by the magnetic force, which the Grad–Shafranov equation expresses.

Leonid Solov’ev found a family of exact solutions in 1968. The art is one of them, ψ = R²Z²/E² + (R² − R₀²)²/4, cut through the ring: each band is one flux surface, hottest at the centre.

The surfaces never cross. Particles stream along them quickly and cross them only slowly, and that is what keeps the heat in.

Nested, never touching.

Equations

\[\Delta^*\psi = -\mu_0R^2\frac{dp}{d\psi} - F\frac{dF}{d\psi}\]
\[\psi = \frac{R^2Z^2}{E^2} + \frac{(R^2-R_0^2)^2}{4}\]
\[\Delta^* = R\frac{\partial}{\partial R}\frac{1}{R}\frac{\partial}{\partial R} + \frac{\partial^2}{\partial Z^2}\]
SymbolMeaningUnit
\(\psi\) poloidal magnetic flux function \(\mathrm{Wb/rad}\)
\(R, Z\) major radius and height \(\mathrm{m}\)
\(R_0\) magnetic axis radius \(\mathrm{m}\)
\(E\) elongation parameter \(\mathrm{1}\)
\(\mu_0\) vacuum permeability \(\mathrm{N/A^2}\)
\(p\) plasma pressure \(\mathrm{Pa}\)
\(F\) RB_\phi, toroidal field function \(\mathrm{T·m}\)
\(\Delta^*\) Grad–Shafranov operator \(\mathrm{m^{-2}}\)

Sources

  1. Grad & Rubin (1958) Hydromagnetic equilibria and force-free fields, Proc. 2nd UN Conf. Peaceful Uses of Atomic Energy 31, 190
  2. Shafranov (1958) On magnetohydrodynamical equilibrium configurations, Sov. Phys. JETP 6, 545
  3. Solov’ev (1968) The theory of hydromagnetic stability of toroidal plasma configurations, Sov. Phys. JETP 26, 400
  4. Freidberg, Ideal MHD (2014), Ch. 6

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