George J. Marklin
A A 523
Course Title: The Physics of Spheromaks. Course Text: 'Spheromaks' by Paul M. Bellan --- Spheromaks are easily formed, self-organized magnetized plasma configurations that are being investigated for their potential to make economical fusion reactors. This course will explain the physics issues underlying their MHD equilibrium and stability and their formation and sustainment using the energy minimization process of Taylor relaxation.
Student learning goals
Describe a spheromak and explain its advantages compared to other fusion reactor candidates such as the FRC, RFP, tokamak and stellerator.
Explain how a spheromak can be made with a magnetized coaxial plasma gun or an inductive helicity injector.
Define magnetic helicity and show that it is conserved in MHD. Show how to generalize it to open systems and derive the helicity evolution equation.
Explain the Taylor minimum energy principle and derive the Taylor state equation curl(B)=lambda*B for both open and closed systems.
Calculate spheromak solutions to the Taylor state equation in cylindrical and spherical geometry.
Explain how the stability of spheromaks depends on geometry, current profiles and plasma beta.
General method of instruction
Classroom lectures and homework. Reading assignments in textbook and selected journal articles.
Students should be familiar with basic plasma physics and basic electricity and magnetism.
Class assignments and grading
Weekly homework and reading assignments.
40% homework 20% midterm exam 40% final exam