# Instructor Class Description

Time Schedule:

**George J. Marklin**

A A 523

Seattle Campus

### Special Topics in Fluid Physics

Offered: AWSp.

**Class description**

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.

**Recommended preparation**

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

*The information above is intended to be helpful in choosing courses. Because the instructor may further develop his/her plans for this course, its characteristics are subject to change without notice. In most cases, the official course syllabus will be distributed on the first day of class.*

Last Update by George J. Marklin

Date: 08/29/2011