Selected Questions -Answers From All Experts Astronomy Forum (Earth flares?)

Question: For the past several yeas I have observed brilliant, colorful flashes in the sky and I have formed a hypothesis that these are Earth flares. Flares similar to the Sun's but occurring on Earth. What do you think of this hypothesis?

Answer:

It is quite possible, though you haven't clarified the atmospheric conditions, that what you've been observing are electrical discharges called "sprites", e.g.

According to a Wikipedia entry: "Sprites are large-scale electrical discharges that occur high above thunderstorm clouds, or cumulonimbus, giving rise to a quite varied range of visual shapes flickering in the night sky. They are triggered by the discharges of positive lightning between an underlying thundercloud and the ground."

In contrast, what we call flares are detected as explosive eruptions on the Sun (solar flares)  in which a vast amount of magnetic potential energy ("free energy") is stored  until released by a process called magnetic reconnection. Technically speaking one need not have magnetic reconnection to qualify for a flare. However, one would need to have at least a magnetic mirror system in place, and this should include structures called double layers, which basically act like capacitors to store electrical energy across large potential drops.

If the voltage drop is large enough, one can observe flare conditions. According to Alfven ('Cosmic Plasma', 1981), any double layers within regional "separators" will explode before a saturation level of current is reached such that:

I_s = [V(b) – V(D)] / R

where V(b) = L(dI/dt) + RI

with L the inductance, and I the current, R the resistance and the flare power can be estimated using:

(P) = I V(D)

where V(D) is the voltage across the double layer. The problem with the Earth flare hypothesis is that it is impossible to see how a magnetic mirror system would operate for it, given the low altitudes at which the phenomenon appeared to be seen by the observer(s) you cite. No magnetic mirrors, no likely Earth flares!

Also, you stated having formed a hypothesis but merely making observations and then a conjecture based on them does not constitute such. What are the key elements of it? How will you test it? What indicators for the test will show the phenomenon is an Earth flare? What observations will you require to support that? What observations will falsify it? What are the necessary and sufficient conditions for an "Earth flare" to occur or exist?

Right now, all you really have is a constellation of peculiar observations or anomalies to which you have attached some significance or physical meaning via intuition (for lack of a better word) but devoid of any formal measurements you yourself have performed. When you perform those measurements, or at least publish the photographs of the assorted phenomena (YOU have taken), I will be more inclined to take "Earth flares" as something substantive and distinct and not merely another UFO manifestation.

Again, 'UFO' is not intended as a putdown, but a simple statement of fact of what you actually have here, minus any compelling data of your own or photos, measurements. These latter might enable a more quantitative basis for analysis and even working out a model for your "Earth flare".

Even if you can't provide a model, you should still be able to at least hypothesize based on observations-data that you yourself obtain. It is all very well to go back to historic sightings, magnetic records, but these still don't make the case that an entity such as an "Earth flare" really exists.

Note also when one uses the term "flare" one means something specific in a context of rapid emission of energy. This applies to every case for a genuine solar flare or what we understand by such.  I see no comparable basis to make a similar claim for Earth  flares.

I encourage you to keep on with your observations of assorted optical phenomena.  In one of my original papers I referred to "transient optical phenomena of the atmosphere" - which paper you might find useful to read, e.g.

http://adsabs.harvard.edu/full/1980JRASC..74..168S

An Introduction to Space Plasma Physics (2)

2)Magnetic mirrors and solar loops

The basic plasma physics for solar active regions usually starts by examining solar coronal loops to see where they conform to the typical magnetic mirror profile used in standard plasma physics. In space physics, one uses the sine of the loss cone angle to obtain the mirror ratio relating the magnetic inductions at the loop ends:

sin (q _L ) = ± Ö (B_min / B _max )

If one finds that there are particles within the “mirrors” for which the “pitch angle” (a) has:

sin (a )  >  Ö (B_min / B _max )

then these will be reflected within the tube, On the other hand, those particles for which the “less than” condition applies will be lost, i.e. on transmission out of the mirror configuration.

Since the adiabatic invariant for particle motion is a constant of the motion:

 m=  ½  [mv ² /B]  

 we have:

 [v _^² /B_max]  =     [v _|| ² /B_z] =    const.  or  

[v _^² / v _|| ²  ]  =  B_z /B_max

Where we take  B_z  = B_min

A simple model for a mirror system is shown below with M1 and M2 the magnetic mirrors separated by a distance L.

If we are careful to change L slowly, then one finds:

 v _|| L = const.

 Now, assume M1 is stationary and M2 moves toward M1 at a velocity,  v _m  , then the incident velocity relative to the wall is:

[(v _||   +  v _m)   -   v _m ]

And:

 

D v _||   =  - [- (v _||   +  v _m)   -   v _m ]  + v _|    =   2 v _m

Thus, with each reflection, the velocity changes by 2 v _m and the number of reflections per second will be:   v _||  / 2L

 Further:

dv _||  /dt  =   2 v _m  (v _||  / 2L)  =  v _||  /L (-dL/dt)

=    - v _||  /L (dL/dt)

So that:   d/dt (v _||  L)  = 0

For kinetic energy of particles we must have:

E   =  ½ m (v_⊥ ²  + v _|| ² ) = const.

Note also that:  v_⊥/ Ω  =   v_⊥/(qB/m) = m v_⊥/qB

Let the guiding center lie on the z-axis (for simplicity) then the average force experienced will be written:

F _z = + ½ q  v_⊥ r _L   (¶B _z/ ¶z) = + ½ q  v_⊥ / Ω _c  ¶B _z/ ¶z

Since:   v_⊥   = r _L  Ω _c     so:  r _L   =  v_⊥/ Ω _c

Where r _L   is the guiding center Larmor radius.

With appropriate substitutions we get:

F _z = + ½ q  v_⊥ r _L   (m v_⊥/qB) (¶B _z/ ¶z) =

+ ½ m v²_⊥ /B  (¶B _z/ ¶z)

But by previous definition for the adiabatic invariant:

m _m  = m(v⊥)²/ 2B  = const .

 So:   F _z =   m  ¶B _z/ ¶z

Where I have dropped the subscript ‘m’.

In relation to solar flare prognostication we are interested in the criterion for the hydrodynamic loss cone instability  which requires that the particular condition for the ratio of untrapped to trapped particles (Pearlstein et al, 1966)[1] :

 n/ n_o  >   2  W _e /  p w _e  =  0.1

where W _e  is the electron cyclotron frequency; and  w _e  is the electron plasma frequency:

w _e     =  [n_e e²/ m_e  ε_o] ^½

Where n_e is the electron number density, e  is the electron charge,  m_e  is the electron mass and ε_o  is the permittivity of free space.

Problems:

1)A proton moves in a uniform electric and magnetic field, with fields given by: E = 10 V/m (x^) and B = 0.0001 T (z^)where '^' denotes vector direction. (Take m _m  = 8.5  x 10 ^-22  J/T)

a) Find the gyrofrequency and the gyro-radius

b) Find the proton's E X B drift speed

c)Find the gyration speed v  and compare  it to the drift speed

d)Find the gyro-period, gyration energy and magnetic moment of the proton.

2) Consider a plasma mirror machine of length 2L with a mirror ratio of 10 so that B(L) = B(-L) = 10 B(0). A group of N (N > 1) electrons with an isotropic velocity distribution is released at the center of the machine. Ignoring collisions and the effect of space charge, how many electrons escape?

3) Consider a similar mirror configuration for a solar coronal loop for which  B_min =   0.2 B_max . Find the loss cone angle for this loop and also determine whether particles will remain within it. Find the velocity  ratio :     

  v _^ / v _||   if    B_max = 0.95 B _z

4) The basic plasma frequency equation relating the ion to the electron plasma frequency can be written:

w ³      =  -  ½ ( w _i ) ² w _e

Find the roots of this equation in terms of the ratio of masses, m _e /m _i.  Show that the real part (or frequency seen in the ion rest frame)  will be:

w _r  =  (½) ^5/3  (m _e /m _i) ^1/3  w _e

Hint:  You may make use of the fact that:

0 =  1 -  w _i  ² / w ^{2   -}-  w _e ² /( w -  w _e ) ²

Where  w _i is the ion plasma frequency and  w _e is the electron plasma frequency

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[1] L.D. Pearlstein, M.N. Rosenbluth, and  D.B. Chang, 1966, Phys. Fluids., Vol. 9, p. 53.