Expert: Philip A. Stahl - 3/19/2008

Question
Can you elaborate a bit about double layers and what role they might play in solar flares? I have been reading an article about them but don't quite get how they work!

Answer
Hello,

If you go back to two questions you asked last year, to do with magnetic mirrors in plasmas, you will see how energy is produced in these situations. In addition, we now know that magnetic mirror effects occur simultaneously with the formation of double layers, in which voltage drops are produced.

What are these double layers?

Basically, a double layer occurs in a plasma and consists of two parallel layers with opposite electrical charge. Think of a capacitor C here)

----------- ++++++
C

----------- (- - - )


A capacitor is a kind of artificial double layer, though it is dramatically different from the type which can occur in solar structures since: i) the latter can also be curved to fit solar loops, ii) the voltages between layers are extremely high - or order 10^9 Volts or more, and iii) the separation dimension is extremely small - on the order of about 100 Debye lengths (according to Volwerk & Kuijpers, Astrophysical Journal Supplement Series, Vol. 90, p. 589, 1994)

The definition of Debye length, for electrons is:

L(De) = (eps_0 k T_e/  n_o q^2)^1/2

where eps_0 is the permittivity of free space (8.85 x 10^-12 F/m), k is the Boltzmann constant (1.38 x 10^-23 J/K), T_e is the electron temperature (~ 10^7 K), n_o is the particle density (e.g. 9.0 x 10^10 /cm^3), and q is the electronic charge).

In solar conditions one distinguishes between "strong" double layers and "weak" ones. Generally, a DL is "strong" provided:

q V(D)/ k T_e  > >   1

where V(D) is the potential drop, q the charge, k the Boltzmann constant and T_e the electron temp. as before.

V(D) appears because in all DLs, the charge cause a strong electric field (E) and a correspondingly sharp change in voltage (electrical potential) across the double layer. Then electrons (or ions) which enter the double layer are accelerated.  They may also be decelerated. Generally, DLs separate regions of plasma with quite different characteristics, for example different densities, Debye lengths, electron temperatures etc.

For solar flares, Hannes Alfven (Cosmic Plasma, 1981, p. 33) energy ought to be minimally generated at the rate:

E/t  =   I V(D)

In the vicinity of typical flares, the current I ~  10^11 A, and as I noted earlier typical potential drops V(D) ~  10^9 V.

Then E/t  ~   (10^11 A) (10^9 V) ~   10^20 J/s

Is this reasonable? A typical optical class 1B H-alpha flare will have an energy of 10^23 J.  It has a duration ~ 1000 s.

So:    10^23 J/  10^3 s  =    10^20 J/s

So, indeed, it is quite reasonable.

Actually physically identifying DLs near flare sites is a whole other project entirely. And because of their small scale (typically on the order of cm) this is indeed difficult. So, the best we can do now is try to look at some key quantitative parameters, and see if magnetic mirrors may be operative  - and then infer the presence of DLs from those.

Hope this helps!