---
title: "Alfvén Waves Interactive Lab | Sandbox Physics"
description: "How can a magnetic field carry a sideways disturbance through a plasma? Bending the magnetic field creates a restoring force that moves the conducting fluid sideways. The disturbance travels along the field as neighbouring fluid responds. A stronger field makes the wave faster; a denser plasma makes it slower."
canonical_url: "https://sandboxphysics.com/labs/alfven-wave/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/alfven-wave/"
last_modified: "2026-10-24"
---

D-X5 · Magnetic tension carries a wave

# Alfvén Waves

**How can a magnetic field carry a sideways disturbance through a plasma?** Bending the magnetic field creates a restoring force that moves the conducting fluid sideways. The disturbance travels along the field as neighbouring fluid responds. A stronger field makes the wave faster; a denser plasma makes it slower.

Pluck a magnetic field line and watch the bend separate into two travelling waves. Strengthen the field or load the plasma with more mass to change their speed.

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

The model solves linear, incompressible shear Alfvén waves parallel to a uniform background field in a periodic domain one hundred megametres long. The displacement is transverse; fluid elements do not travel along the field with the wave. Magnetic field perturbations follow the displacement gradient, and the model calculates kinetic and magnetic perturbation energy from that same solution. Packet profiles use twelve exact Fourier modes; periodic copies re-enter the opposite side. The displayed transverse displacement is enlarged fourteen times. Playback advances one hundred and eighty model seconds per real second. The density is uniform, the fluid is perfectly conducting, and the small physical slope stays within the linear approximation. Compressible waves, resistivity, viscosity, kinetic effects, reconnection, curved solar loops and observed solar data are omitted.

Simulated data

## Where the wave stores its energy

Local kinetic and magnetic perturbation energies come from the same wave solution.

> Interactive plot of the simulated thermal or magnetic model.

Kinetic energy

Magnetic perturbation energy

## Where the idea came from

[A bent magnetic field can carry a wave](https://sandboxphysics.com/stories/thermal-complexity/alfven-magnetic-tension/) [Explore heat, chance and collective behaviour](https://sandboxphysics.com/stories/thermal-complexity/)

Physics tutorial

## A bent field pulls a conducting fluid back

**Background** A perfectly conducting fluid carries the magnetic field with it. Move the fluid sideways and the field bends; the resulting magnetic force tends to straighten it.

**Why it matters** This restoring force makes a wave whose speed depends on magnetic field and mass density. It adds physics that an ordinary fluid wave does not contain.

Start with the essentials

- **Focus question**: Does a stronger field or a heavier plasma transmit the disturbance faster?
- **One-sentence intuition**: Magnetic tension speeds the wave up; the inertia of the plasma slows it down.

### Core mathematical model

#### The speed of a parallel shear Alfvén wave

$$
v_A=\frac{B_0}{\sqrt{\mu_0\rho}}
$$

The background magnetic field sets the restoring force and mass density sets the inertia. The displayed field is in microtesla and density is in trillionths of a kilogram per cubic metre.

#### One displacement determines both velocity and magnetic bending

$$
v_\perp=\frac{\partial\xi}{\partial t},\qquad b_\perp=B_0\frac{\partial\xi}{\partial x}
$$

Position along the background field is horizontal. Fluid displacement is transverse. A travelling bend need not carry a fluid element along with it.

#### Kinetic and magnetic perturbation energies

$$
u_K=\frac12\rho v_\perp^2,\qquad u_B=\frac{b_\perp^2}{2\mu_0}
$$

The plot below shows local wave-energy density, excluding the unperturbed background field. In the periodic ideal model, their integrated sum stays constant.

### Common difficulties

#### The wave moves along the field; the fluid moves across it

**Typical misconception** A bright fluid element must travel down the field line with the pulse.

**Better mental model** The element oscillates sideways around its own horizontal position. The changing bend passes from one element to the next.

### Run the experiment

1. 01

   #### Release a sideways bend

   Choose One pluck, two waves, or drag the bright field line and release it.

   **What to observe:** A displacement released from rest separates into two waves moving in opposite directions.

2. 02

   #### Change the restoring force

   Keep the density fixed and double Magnetic field.

   **What to observe:** The same disturbance crosses the domain in half the time.

3. 03

   #### Add inertia

   Compare One pluck, two waves and A heavier plasma.

   **What to observe:** Quadrupling density halves the speed. The brighter fluid markers still move across the field, not along it.

4. 04

   #### Watch energy exchange

   Choose A standing wave and compare the energy-density curves below.

   **What to observe:** The wave alternates between magnetic bending and fluid motion. Total perturbation energy is conserved.

Physical conclusion

Alfvén waves carry transverse motion along a magnetic field through the combined action of magnetic tension and fluid inertia.

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)