• Alfvena Alfvén Waves pixel-art physics T-shirt, white tee, front view

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Alfvena

Alfvén Waves Physics

\[v_A = \frac{B}{\sqrt{\mu_0 \rho}}\]
$29.99 USD
$29.99 USD
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Size guide S–5XL · inches

Alfvena plays the Sun like a harp. Every magnetic field line is a taut string, and when she plucks one, the plasma sings.

The Physics

In a plasma, magnetic field lines behave like stretched strings. Shake one sideways and a transverse ripple runs along it, carrying the plasma with it. This is the shear Alfvén wave of ideal magnetohydrodynamics, and its speed is set by the field strength and the plasma's density.

v_A = B / √(μ₀ρ) and ω = k∥ v_A

  • v_A: Alfvén speed (m/s)
  • B: magnetic field (T)
  • μ₀: vacuum permeability (H/m)
  • ρ: plasma mass density (kg/m³)
  • ω: angular frequency (rad/s)
  • k∥: wavenumber along B (1/m)

Hannes Alfvén predicted these waves in Nature in 1942 and shared the 1970 Nobel Prize in Physics for his work in magnetohydrodynamics.

Honest caveat: The Sun's corona is about 1–2 million K while its surface is about 5800 K. Alfvén waves are a leading candidate for heating it, but the question is still open.

On the shirt

Front: Alfvena, the pixel-art character, with the title. Back: the field-line strings, both Alfvén equations, the coronal-heating note and Alfvén's 1942 paper. Printed on a unisex tee.

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

Details

Size & fitS–5XL

Unisex heavy cotton (Gildan 5000), classic fit.

SizeWidthLengthSleeve
S182815.1
M202916.5
L223018
XL243119.5
2XL263221
3XL283322.4
4XL303423.7
5XL323525

スケール感の目安：サイズ M の幅は 20 in（50.80 cm）で、プランク長のおよそ 3.143 × 1034 倍です（lP = 1.616255 × 10−35 m）。メジャーで測るほうが早いです。

Measurements in inches, ±1.5 in tolerance.

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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

I play the Sun like a harp. In a plasma, magnetic field lines behave like taut strings: the field's tension pulls back on any bend, and the plasma tied to the lines gives them mass.

Pluck one sideways and a ripple runs along it at the Alfvén speed, B/√(μ₀ρ). Stronger field, faster wave; denser plasma, slower. For the shear Alfvén wave of ideal magnetohydrodynamics the frequency is just k∥ v_A, set only by the wavelength along the field. Hannes Alfvén predicted these waves in Nature in 1942 and shared the 1970 Nobel Prize in Physics.

Here is my open question. The Sun's surface is about 5800 K, yet its corona is about 1 to 2 million K. My waves carry energy upward and are a leading candidate for heating it, but how the corona is heated is still not settled.

Equations

\[v_A = \frac{B}{\sqrt{\mu_0 \rho}}\]
\[\omega = k_{\parallel}\, v_A \qquad (\text{shear Alfvén wave, ideal MHD})\]
SymbolMeaningUnit
\(v_A\) Alfvén speed \(\mathrm{m/s}\)
\(B\) magnetic field \(\mathrm{T}\)
\(\mu_0\) vacuum permeability \(\mathrm{H/m}\)
\(\rho\) plasma mass density \(\mathrm{kg/m³}\)
\(\omega\) angular frequency \(\mathrm{rad/s}\)
\(k_{\parallel}\) wavenumber along the magnetic field \(\mathrm{1/m}\)

Sources

  1. Alfvén (1942) Existence of Electromagnetic-Hydrodynamic Waves, Nature 150, 405
  2. Nobel Prize in Physics 1970, Hannes Alfvén, NobelPrize.org
  3. De Pontieu et al. (2007) Chromospheric Alfvénic Waves Strong Enough to Power the Solar Wind, Science 318, 1574

Field notes

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