mathematics

Harold Weitzner

Harold Weitzner 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 Harold Weitzner rather than just read about it. In short: Harold Weitzner is an American applied mathematician and physicist whose primary research is plasma physics. He is Professor Emeritus of Mathematics at the Courant Institute of Mathematical Sciences and has served as Director of the Magneto-Fluid Dynamics Division at Courant since 1981, succeeding Harold Grad.

Key takeaways

Harold Weitzner belongs to mathematics; place it in that map before memorising details.
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Reproduce the core statement of Harold Weitzner from memory before moving on to harder problems.

Reference excerpt

Harold Weitzner is an American applied mathematician and physicist whose primary research is plasma physics. He is Professor Emeritus of Mathematics at the Courant Institute of Mathematical Sciences and has served as Director of the Magneto-Fluid Dynamics Division at Courant since 1981, succeeding Harold Grad. He has published over 120 research articles on the topics of plasma physics, magnetohydrodynamics, fluid mechanics, fractional equations and kinetics, and chaos. Professor Weitzner received his Ph.D. in 1958 from Harvard University on the topic of "Hyperon-Nucleon Interactions". In 1981 he was elected a Fellow of the American Physical Society.

Selected publications Weitzner, Harold. "Green's function for the linearized Vlasov equation." The Physics of Fluids 5.8 (1962): 933–946. Cumberbatch, E., L. Sarason, and H. Weitzner. "Magnetohydrodynamic flow past a thin airfoil." AIAA Journal 1.3 (1963): 679–690. Weitzner, Harold. "Plasma oscillations and Landau damping." The Physics of Fluids 6.8 (1963): 1123–1127. Weitzner, Harold. "Green's Function for the Linearized One‐Dimensional Krook Equation with Electric Forces." The Physics of Fluids 6.4 (1963): 484–490. Weitzner, Harold. "Long-Wavelength Plasma Oscillations." Physics of Fluids 7 (1964): 476–477. Weitzner, Harold. "Radiation from a Point Source in a Plasma." The Physics of Fluids 7.1 (1964): 72–89. Weitzner, Harold. "Exponential damping of collisionless plasma oscillations." Communications on Pure and Applied Mathematics 18.1‐2 (1965): 307–311. Weitzner, Harold. "Extension of the Penrose Condition." The Physics of Fluids 9.3 (1966): 624–626. Weitzner, Harold, "Longitudinal Plasma Oscillations" in Magneto-fluid and plasma dynamics, Proceedings of a Symposium in Applied Mathematics, & American Mathematical Society (AMS, 1967) Weitzner, H., and D. Dobrott. "Ion waves in a collisionless plasma." The Physics of Fluids 11.1 (1968): 152–157. Blank, A. A., H. Grad, and H. Weitzner. "Toroidal High-β Equilibria." Plasma Physics and Controlled Nuclear Fusion Research. Proceedings of the Third International Conference on Plasma Physics and Controlled Nuclear Fusion Research. Vol. II. 1969. Grad, Harold, and Harold Weitzner. "Critical β from Stellarator and Scyllac Expansions." The Physics of Fluids 12.8 (1969): 1725–1727.

Marder, B., and H. Weitzner. "A bifurcation problem in E-layer equilibria." Plasma Physics 12.6 (1970): 435. Weitzner, Harold. "Free boundary long helical wavelength equilibria." The Physics of Fluids 14.3 (1971): 658–670. Weitzner, Harold. "Growth rates and spectra for a particular axially symmetric equilibrium." The Physics of Fluids 16.2 (1973): 237–246. Freidberg, J. P., B. M. Marder, and H. Weitzner. "Stability of diffuse high-beta helical systems." Nuclear Fusion 14.6 (1974): 809. Freidberg, and H. Weitzner. "Endloss from a linear θ-pinch." Nuclear Fusion 15.2 (1975): 217. Weitzner, Harold. "Comparison of unstable modes and growth rates in ideal magnetohydrodynamics and guiding center plasmas." The Physics of Fluids 19.3 (1976): 420–426. Weitzner, Harold. "Steady plasma flow with a shock in a mirror." The Physics of Fluids 20.8 (1977): 1289–1295. Weitzner, Harold. "End loss from a theta pinch." The Physics of Fluids 20.3 (1977): 384–389. Weitzner, Harold, and Donald B. Batchelor. "Conversion between cold plasma modes in an inhomogeneous plasma." The Physics of Fluids 22.7 (1979): 1355–1358.

Weitzner, Harold, and D. B. Batchelor. "An eikonal expansion of the Vlasov–Maxwell equations valid near cyclotron resonance." The Physics of Fluids 23.7 (1980): 1359–1367. Weitzner, Harold. "Motion of a charged particle in a nearly axisymmetric magnetic field." The Physics of Fluids 24.12 (1981): 2280–2294. Berk, Herbert L., James H. Hammer, and Harold Weitzner. "Analytic field-reversed equilibria." Physics of Fluids 24 (1981): 1758–1759. Weitzner, Harold. "Linear wave propagation in ideal magnetohydrodynamics." Basic plasma physics. 1. 1983. Weitzner, Harold. "Motion of a charged particle in slowly varying electromagnetic fields." Communications on pure and applied mathematics 36 (1983). Batchelor, D. B., R. C. Goldfinger, and Harold Weitzner. "Propagation and absorption of electromagnetic waves in fully relativistic plasmas." The Physics of fluids 27.12 (1984): 2835–2846. Grossmann, William, and Harold Weitzner. "A reformulation of lower‐hybrid wave propagation and absorption." The Physics of fluids 27.7 (1984): 1699–1703. Hirshman, S. P., and H. Weitzner. "A convergent spectral representation for three‐dimensional inverse magnetohydrodynamic equilibria." The Physics of fluids 28.4 (1985): 1207–1209. Weitzner, Harold. "Lower hybrid waves in the cold plasma model." Communications on pure and applied mathematics 38.6 (1985): 919–932. Amendt, Peter, and Harold Weitzner. "Relativistically covariant warm charged fluid beam modeling." The Physics of fluids 28.3 (1985): 949–957. Weitzner, Harold, and Wolfgang Kerner. "Tokamak transport based on the Braginskii model." Zeitschrift für Naturforschung A 42.10 (1987): 1101–1114. Jaeger, E. F., D. B. Batchelor, and H. Weitzner. "Exact and approximate solutions to the finite temperature wave equation in a one-dimensional perpendicularly stratified plasma." Nuclear fusion 28.1 (1988): 53. Weitzner, Harold, and William S. Lawson. "Boundary conditions for the Darwin model." Physics of Fluids B: Plasma Physics 1.10 (1989): 1953–1957. Weitzner, Harold. "Relativistic Plasmas" in Relativistic Fluid Dynamics (Springer, 1989) pp 211–237.

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Worked examples

Example 1 — a first encounter with Harold Weitzner

Start with the simplest possible case. Write down what Harold Weitzner 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 Harold Weitzner 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 Harold Weitzner 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 Harold Weitzner

In research: Harold Weitzner 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 Harold Weitzner 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: Harold Weitzner is common in secondary-school and first-year university syllabi. It links to neighbouring topics 20th-century American mathematicians, American physicists, Courant Institute of Mathematical Sciences faculty, so understanding it makes those chapters shorter.
In everyday life: Look for Harold Weitzner 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 Harold Weitzner in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Harold Weitzner 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.
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Frequently asked questions

What is Harold Weitzner in simple terms?

Why does Harold Weitzner 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 Harold Weitzner?

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 Harold Weitzner.