# The possibility of IEC and Earnshaw's theorem

1. May 27, 2013

### Boltzmann2012

Hi all,

I recently read about a Fusor, on wikipedia and to my surprise there has been lots of research going on Inertial Electrostatic Confinement. I actually have a query, I quote from D.J.Griffiths, Electrodynamics Third Edition, pp 115

"Earnshaw's theorem says that electrostatic containment is also out of the question. Fortunately, it is possible to confine a hot plasma magnetically."

I think magnetic confinement was confirmed by Alfven's theorem.
How do you explain the possibility of IEC when its very existence is ruled out by Earnshaw?

2. May 27, 2013

Staff Emeritus
Do you know how IEC works? Can you formally state Earnshaw's theorem?

3. May 27, 2013

### Boltzmann2012

Earnshaw's theorem states that a charged particle cannot be held in stable equilibrium by pure electrostatic forces alone. If you have a cube of positive charges you cannot place a positive charge at the center in stable equilibrium.

As far as I can see, my only confusion is that, Griffiths clearly says,

"To harness nuclear fusion as a practical energy source it is necessary to heat the plasma(soup of charged particles) to fantastic temperatures. Earnshaw's theorem states that electrostatic confinement is also out of the question."

Is an IEC more than just what I think it is?

Regards,
Boltzmann

4. May 28, 2013

### the_wolfman

The answer is in the name IEC... Inertial Electrostatic Confinement.

IEC uses electrostatic forces to accelerate and focus ions into a dense core. The acceleration is key, and it is not a equilibrium process from the particle standpoint. Thus Earnshaw's theorem does not apply.

Are you talking about the Frozen Flux Theorem? While extremely useful, I would not say that it confirmed magnetic confinement.

5. May 28, 2013

### Boltzmann2012

In that case, it doesn't even qualify to be a confinement method, I suppose.

6. May 28, 2013

### the_wolfman

Why do you say that?

The radial beam of ions has a dynamical pressure $n_i m_i V_r^2/2$ that can be used to confine a plasma.

Inertial confinement concepts rely of this dynamical pressure to confine the plasma.

Traditionally inertial confinement creates the radially directed velocity by ablating the surface of a target pellet. The outer surface heats up and is blown off of the target. Much like a rocket, due to the conservation of momentum this blow off produces a large inward force on the pellet.

Instead of relying on this rocket effect, Inertial Electrostatic confinement uses a potential difference to accelerate ions inwards.

In both cases, it is the same dynamical pressure that supports the high temperature high density core, but the driver mechanism that it in the two cases is very different.

7. May 28, 2013