The Electron Plasma Trap
Graduate Student Researchers
In our Malmberg-Penning
trap, we confine only electrons. An inject,
hold and dump cycle is used to regulate the flow of electrons into
and out of the trap. A modified trap may allow neutral plasmas to
be trapped. A double well trap is a possible solution to the problem
of confining a neutral plasma in a Malmberg-Penning
A Malmberg-Penning trap with suitably applied gate potentials (fig. 1a)
may be used to confine oppositely charged species. The negatively
charged particles will fall into the central well (fig. 1b) and the positively
charged particles will be trapped inside the outer potential walls (fig.
1c). Electron-positron dynamics and anti-hydrogen production could
be studied in this trap.
One of the difficulties in using double well neutral plasma traps is
the separation of the particles into their respective wells, thereby filling
the wells and unmixing the species. In addition, the filled wells
might contain enough charge to shield out the potential and allow the other
species to escape.
We will discuss several schemes which may remedy this problem.
We will also present calculations of plasma heating relevant to these schemes,
and experimental results.
Figure 2 shows that the plasma drops into and fills wells in a time on
the order of 100 ms. This is a collisional time scale rather than
an instability time scale. Consequently, we must act on a time scale of
less than 100 ms to maintain a neutral plasma regime.
Two possible approaches to preventing the problems associated with the
filled wells are presented in this poster. The first is to resonantly
drive particles out of the well. The second is to periodically create
new empty wells to replace the wells as they fill.
Three methods for replacing a filled well with an empty one are:
Moving an empty well into the plasma.
Creating a stationary empty well outside the plasma, and allowing the plasma
to flow into that well.
Instantaneously creating a new well within the plasma.
The Moving Well
One method for replacing a filled well is to have an empty well move into
the plasma, replacing the filled well. As the moving well enters
the plasma, we expect it to be antishielded and thus remain empty. We
have successfully observed this antishielding in our experiment.
The following sequence of diagrams shows the on-axis potential along the
trap used for a moving well.
The Static Well
Another method is to compress the plasma, create an empty well outside
of the plasma, and let the plasma expand to its original length (fig. 4).
The Instantaneous Well
Yet another possibility is to instantaneously create a well within
the plasma. Because the well is created instantaneously, it will be relatively
unfilled. This well is then moved over to take the place of the filled
An alternative to creating a new well is to continuously drive particles
out of the well as it fills. In the ideal case of a harmonic well,
particles could be ejected from the well by driving them at the resonant
frequency. Unfortunately, it may be difficult to make a purely harmonic
well, as the charge distribution of the plasma itself will perturb the
applied potential. In the more likely scenario of an anharmonic well,
noise could be used to stochastically drive particles out of the well.
All of these methods are plagued by excessive heating. In the course
of the plasma manipulations, there are various adiabatic heating and cooling
cycles. Additionally, there are free expansions which heat the plasma.
We find that in our experiments with the moving well and the static well
there is net heating. It seems likely that there will also be net
heating for the instantaneous well and the tickled trap. This may
prohibit the useful application of these techniques to neutral plasma trapping.
We considered two models of free expansion heating. The first
model compares the electrostatic potential energy of an electron column
before and after an expansion into a region without a well. The decrease
in potential energy results in a temperature increase,
C is a constant, L is the length of the plasma and n is the density.
For typical parameters in our experiment, this formula yields DkT
~ 3 eV.
The second model is a single particle model in which we ignore the plasma
self-potential. Electrons are considered to be moving in the applied
gate potential and to obey the Boltzmann distribution. The following
equation, which results from the conservation of energy and particle number,
must be solved to find the final temperature.
where x is ef/kT, f
is the well depth and Lw is the length of the well. Typical
values are on the order of 10 eV.
In experiments with the static well, we find net heating for a range
of initial densities and well depths (fig. 6). Substantial heating
was also observed for the moving well.
In order to confine both positive and negative charges within a Malmberg-Penning
trap, the schemes described in this poster may not be adequate. While
we can succeed in replacing the filled wells with empty wells, the amount
of plasma heating may preclude the application of these techniques.