Slide through the integral!

j(r’) r’ ur’ - r + B(r) r

R z’ r dz’ 2 L I B z

R z’ r dz’ 2 L I B z

summary jsjs Three techniques to find B 1] Ampere’s circuital law - lots of symmetry 2] find vector potential A, then B =  x A 3] Biot - Savart law B A BB

magnetic forces x y z B V F+ F- Lorentz force

B v MaMa MbMb

Please Note: Rocket Sets contain rocket motors that are classified as hazardous materials for shipping purposes. Given this, we must ship Rocket Sets via surface mail through the USPS.

MHD w plasma drift w F = Q (E + v x B) = 0 w 0 = E  x + v B  x w  V  v B  x C B B

electric power in space! 12 miles

plasma physics NSNS NSNS

NSNS

magnetic field particle loss

Example: Charged Particle Orbits in a Tokamak finite element method FEMLAB using MATLAB

poloidal coils transformer core B IpIp I coil primary winding Tokamak principle Tokamak – Problem Definition

Introduction w A tokamak is a “magnetic bottle” for the confinement of high energy plasmas in Controlled Nuclear Fusion. w The ions and electrons in the plasma travel far between collisions. collisionless model particle motion is governed by the EM field losses are mainly due to collisions with the walls Tokamak

Modeling approach w Coils and plasma current are modeled in FEMLAB and the magnetic field is computed. plasma current = 2.2 MA peak toroidal magnetic field = 2 T w Particle orbits are computed using an ODE solver. Tokamak

Results – particle simulation Proton orbit - Results banana orbits

work x y z B V F

VIS Dr. Lou Frank & Dr. John Sigwarth

1 I 1 dl 1 B2B2 I 2 dl 2 B1B1

lightning arrestor or STAR WARS

Magnetic resonance imaging?

electric machines rotate about an axis no translation torque

 (forces) z x y I yy B xx

Torque   + y z B yy  x

Never Use Detergent Again! What would you say if I told you that one of the great inventions of the modern age has no moving parts, doesn't have anything to do with the Internet, doesn't even use Microsoft software? What is this wondrous invention... the Euro-Wash Laundry Ball... a collection of rubber and magnets that cleans clothes, even in the hardest of waters without soaps or detergents. Euro-Wash Laundry Ball

MagneForce The first shoe with its own power supply. Comfortable, quality footwear constructed with a lightweight, flexible magnetic insole to generate a deep penetrating magnetic field which increases circulation; reduces foot, leg, and back fatigue; provides natural pain relief and improved energy level. The James Randi Educational Foundation offers $1 million to Florsheim if it can demonstrate its claims for MagneForce Footwear in a formal double-blind scientific test.

Variable Specific Impulse Magnetoplasma Rocket The VASMIR engine has three magnetic cells. 1) Hydrogen is ionized. 2) Microwaves heat the plasma. 3) Magnetic nozzle converts energy into a directed flow. Mars, here we come! cnn 6/2000

1) Hydrogen is ionized. 2) Microwaves heat the plasma. 3) Magnetic nozzle converts energy into a directed flow.

1) Hydrogen is ionized. 2) Microwaves heat the plasma. 3) Magnetic nozzle converts energy into a directed flow.

1) Hydrogen is ionized. 2) Microwaves heat the plasma. 3) Magnetic nozzle converts energy into a directed flow.