Coulomb term in Potential of ions in a Penning Trap,Green's Function

In summary, the conversation discusses the use of Green's function for writing the inter-ionic Coulomb interaction in a Penning trap. The participants also mention the use of image charges in the electrodes and the applicability of the simple expression of all Coulomb pairs. They also mention the application of Green's method for solving differential equations.
  • #1
aim1732
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How do you write out the potential of an ion in a Penning trap? Specifically, how does the inter-ionic Coulomb interaction come to be written as a Green's function? I found it here : http://journals.aps.org/rmp/pdf/10.1103/RevModPhys.71.87

They do say something about interactions with image charges in the electrodes, but I can not see why a simple expression of all Coulomb pairs is not good enough. They seem to use it well enough in some of the other papers I read.
 
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  • #2
Green's function in E&M just means the the integral k rho/|r-r'| over r' where rho is the change density.

A greens method is a nifty way of solving differential equations by convolving something with the green function. The Green function typically have the form f(r-r').
 

What is the Coulomb term in the potential of ions in a Penning Trap?

The Coulomb term in the potential of ions in a Penning Trap refers to the electrostatic potential energy between charged particles within the trap. It takes into account the repulsive or attractive forces between the ions due to their charges.

How does the Coulomb term affect the behavior of ions in a Penning Trap?

The Coulomb term plays a crucial role in determining the equilibrium position and stability of ions in a Penning Trap. It influences the motion of ions and can cause them to oscillate or spiral inwards or outwards, depending on the strength of the electrostatic forces.

What is the Green's function in the context of a Penning Trap?

The Green's function in the context of a Penning Trap is a mathematical function that describes the relationship between the external electric potential and the resulting distribution of ions within the trap. It is used to solve the Poisson equation for the electric potential in the trap.

How is the Coulomb term calculated in the potential of ions in a Penning Trap?

The Coulomb term is calculated by summing up the individual Coulomb potential energies between each pair of ions within the trap. This is done using the Coulomb's law, which states that the force between two charged particles is inversely proportional to the square of the distance between them.

Can the Coulomb term be neglected in the potential of ions in a Penning Trap?

No, the Coulomb term cannot be neglected as it is a significant component of the potential energy in the trap. Neglecting it would result in an inaccurate description of the behavior of ions in the trap and could lead to incorrect predictions of their motion and stability.

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