mathematics

Lundquist number

Lundquist number is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Lundquist number rather than just read about it. In short: In plasma physics, the Lundquist number (denoted by S {\displaystyle S} ) is a dimensionless ratio which compares the timescale of an Alfvén wave crossing to the timescale of resistive diffusion. It is a special case of the magnetic Reynolds number when the Alfvén velocity is the typical velocity scale of the system, and is given by S = L v A η , {\displaystyle S={\frac {Lv_{A}}{\eta }},} where L {\displaystyle L} i…

Key takeaways

Lundquist number belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Lundquist number to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Lundquist number from memory before moving on to harder problems.

Reference excerpt

In plasma physics, the Lundquist number (denoted by S {\displaystyle S} ) is a dimensionless ratio which compares the timescale of an Alfvén wave crossing to the timescale of resistive diffusion. It is a special case of the magnetic Reynolds number when the Alfvén velocity is the typical velocity scale of the system, and is given by

S = L v A η , {\displaystyle S={\frac {Lv_{A}}{\eta }},}

where L {\displaystyle L} is the typical length scale of the system, η {\displaystyle \eta } is the magnetic diffusivity and v A {\displaystyle v_{A}} is the Alfvén velocity of the plasma. High Lundquist numbers indicate highly conducting plasmas, while low Lundquist numbers indicate more resistive plasmas. Laboratory plasma experiments typically have Lundquist numbers between 102–108, while in astrophysical situations the Lundquist number can be greater than 1020. Considerations of Lundquist number are especially important in magnetic reconnection.

See also Magnetic Prandtl number Péclet number Stuart number

References Priest, Eric; Forbes, Terry (2000), Magnetic Reconnection (PDF), Cambridge University Press, ISBN 978-0-521-48179-3

Worked examples

Example 1 — a first encounter with Lundquist number

Start with the simplest possible case. Write down what Lundquist number claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Lundquist number before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Lundquist number ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Lundquist number

In research: Lundquist number appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Lundquist number in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Lundquist number is common in secondary-school and first-year university syllabi. It links to neighbouring topics Plasma parameters, Plasma physics stubs, so understanding it makes those chapters shorter.
In everyday life: Look for Lundquist number outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Lundquist number in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Lundquist number means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Lundquist number out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Lundquist number in simple terms?

Why does Lundquist number matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Lundquist number?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Lundquist number.