This allows us to grasp the nature of the forces working in a plasma. It will not make it any more predictable but we at least know why and know that all modeling must be subjected to real conditions as well. We may never need to be much better than that either.
What is clear though is just how expandable all this becomes. Thus we see the clear creations of plasmas when we look at the stars and galaxies been demonstrated there.
Essential Guide to the EU – Chapter 4 Electromagnetism
Calculate all the forces acting on each particle via Lorentz Law
Calculate new locations and velocities for a very short increment of time using Newton’s Laws of Motion
Calculate E and B at each charged particle’s new location after this time increment
If an End-Loop condition is not satisfied yet, go back to 1. and continue calculating
Other aspects can be added in for greater accuracy or a better approximation to “reality”, such as collisions of particles, viscous and gravity forces, etc. for more complete modeling. This is a complex undertaking, and large models with many particles may take months of supercomputer time to run.
- A static electric field can exist in the absence of a magnetic field; e.g., a capacitor or a dust particle with a static charge Q has an electric field without a magnetic field.
- A constant magnetic field can exist without an electric field; e.g., a conductor with a constant current I has a magnetic field without an electric field.
- Where electric fields are time-variable, a nonzero magnetic field must exist.
- Where magnetic fields are time-variable, a nonzero electric field must exist.
- Magnetic fields can only be generated in two ways other than by permanent magnets: by an electric current, or by a changing electric field.
- Magnetic monopoles cannot exist; all lines of magnetic flux are closed loops.
It is like an arrow: it has a length and it points in a direction. By contrast, a scalar quantity only has magnitude. Examples include speed and temperature. Vector algebra is the mathematics which deals with vectors. For those wanting to know, further details of vector algebra are given in Appendix III.
The Hyperphysics explanation is also a good introduction. The essentials for understanding the Lorentz equation will be explained here.
A simplified example is increasing the speed of a car to three times its initial speed as it moves in a straight line. Imagine that the car’s velocity vector is simply an arrow pointing straight ahead down the roadway, with its base or starting point always at the center of the car. Picture this arrow as being 20 cm long to represent a starting speed of 20 km/hour. Then you push down on the accelerator pedal to make the wheels of the car turn faster and push (accelerate) the car to a higher speed. As the car speeds up, the length of the arrow increases so that it always matches the car’s speed. At 60 km/hour the arrow is 60 cm long, and its direction is still parallel to the roadway. If you press the brake pedal, the car accelerates in the opposite direction, slowing down, and the arrow becomes shorter and shorter. As the car stops, its speed drops to zero, and the velocity arrow or vector becomes zero in length.
“That is easy to understand”, you say. “What happens if I turn the steering wheel to, say, the left?” That kind of an action introduces an additional force on the car, in a different direction from that pointing parallel to the centerline of the car.
It does not increase or decrease its speed (neglecting friction!) but something changes because the car is turning! The velocity vector from the wheels making it go 60 km/hour has not changed length, but an additional force in a different direction has been applied, so now the velocity vector becomes the result of two different forces (two arrows acting on the center of the car). As long as you hold the steering wheel at the same angle, the same force is being applied that wants to turn the car, and it moves around on a circle at a constant speed.
As in the case of our screw, if the vectors are aligned (parallel) in the first place, then no movement of the screw takes place. The cross product of aligned vectors is zero.
- Electric fields cause a force on all charged particles.
- The electric force will be in opposite directions for oppositely charged particles; therefore, an electric field will produce opposite velocities of ions and electrons and so tend to separate them. Charge separation in space is important in plasma physics.
- Magnetic fields only act on moving charged particles having a component of motion perpendicular to the magnetic field. Because the force depends on the cross-product of the velocity and field vectors, the effect will be different in different directions. This results in a direction-dependent electrical resistance. Think of trying to swim straight across a river rather than with the water’s current.
- The direction of the magnetic force is momentum and charge-dependent; ions and electrons will therefore circle in opposite directions with different radii and periods of rotation.
- Bulk plasma moving across the direction of a magnetic field will cause a local electric field to develop which itself will cause new forces on the charged particles.
- Changes in the distribution of charged particles cause a change in the electric field between them; a changing electric field generates a change in the magnetic field.
- The Maxwell Equations and the Lorentz Force Law act together as a feedback loop modifying the motions of the charged particles and the fields in complex ways.