Mmmm... science content??
The charging and discharging of the leyden jar not sciencey enough for ya!
Maybe you'd like to partake in a little experimental "science"? You know hands on, getting into it, scientific experiment, much like I show my 4 yr old daughter
I'd love nothing more to give you a mathematical description of an electric discharge but does one in fact exist?
But the leyden jar "scientific" experiment should get the point across with no need to resort to some differe
ntia
tal ve
Ctor integ
ral!!
Obviously there would be a number of very dynamic variables at play in an event such as this so I'm not sure what you maths is going to
PROVE!!
All right I'm no mathematician but lets have a crack at a little mathmatical jiggery pokery, I'm sure if I do something wrong someone here will let me know!
In relation to the spider crater on Mercury being an electrical discharge (spark/arc) phenomena and not impact, volcanic or geological. Then we might just be able to do some maths.
Ok lets work out some basics
Electrostatic discharge (spark/arc)
Electrostatic discharge (ESD) is the sudden and momentary electric current that flows between two objects at different electrical potentials caused by direct contact or induced by an electrostatic field.
Futher from the same article
Sparks
Main article: corona discharge
A spark is triggered when the electric field strength exceeds approximately 10 – 30 kV/cm[citation needed] (the dielectric field strength of air). This may cause a very rapid increase in the number of free electrons and ions in the air, temporarily causing the air to abruptly become an electrical conductor in a process called dielectric breakdown.
Perhaps the best known example of a natural spark is a lightning strike. In this case the potential difference between a cloud and ground, or between two clouds, is typically hundreds of millions of volts. The resulting current that flows through the ionized air causes an explosive release of energy. On a much smaller scale, sparks can form in air during electrostatic discharges from charged objects that are charged to as little as 380 volts (Paschen's law).
so as we are not talking about the dielectric field strength of
air here but of space/vacuum would could roughly generalize with the
electric constant
or
But that's not of much help if what we a really after is
Realization of free space in outer space
While only a partial vacuum, outer space contains such sparse matter that the pressure of interstellar space is on the order of 10 pPa (1×10−11 Pa)[31]. For comparison, the pressure at sea level (as defined in the unit of atmospheric pressure) is about 101 kPa (1×105 Pa). The gases in outer space are not uniformly distributed, of course. The density of hydrogen in our galaxy is estimated at 1 hydrogen atom/cm3.[32] The critical density separating a Universe that continuously expands from one that ultimately crunches is estimated as about three hydrogen atoms per thousand liters of space.[33] In the partial vacuum of outer space, there are small quantities of matter (mostly hydrogen), cosmic dust and cosmic noise. See intergalactic space. In addition, there is a cosmic microwave background with a temperature of 2.725 K, which implies a photon density of about 400 /cm3.[34] [35]
The density of the interplanetary medium and interstellar medium, though, is extremely low; for many applications negligible error is introduced by treating the interplanetary and interstellar regions as "free space".
So while we are not talking about IPM or ISM here at Mercuries orbit what is actual plasma density there?
If it's coupled to the solar wind then it's going to be highly variable, I would imagine considering how dynamic the solar wind is (Sun plasma stream).
So which electric constant shall we "pick"?
Anywhoo... according to my theory once a threshold was reached WRT charge separation and electric field strength and the electric constant a
corona discharge started.
Firstly
In electricity, a corona discharge is an electrical discharge brought on by the ionization of a fluid surrounding a conductor, which occurs when the potential gradient (the strength of the electric field) exceeds a certain value, but conditions are insufficient to cause complete electrical breakdown or arcing.
That fluid in this case is plasma, remember we are on Mercuries surface here.
Now I believe that the conditions that contributed to the formation of this "spider crater" continued to increase the strength of the local electric field so
If the geometry and gradient are such that the ionized region continues to grow instead of stopping at a certain radius, a completely conductive path may be formed, resulting in a momentary spark, or a continuous arc.
So the steps that involved are quite straight forward.
Pretty pics omitted for the sake of bandwidth
Mechanism of corona discharge:
Corona discharge of both the positive and negative variety have certain mechanisms in common.
1. A neutral atom or molecule of the medium, in a region of strong electric field (such as the high potential gradient near the curved electrode) is ionized by an exogenous environmental event (for example, as the result of a photon interaction), to create a positive ion and a free electron.
2 The electric field then operates on these charged particles, separating them, and preventing their recombination, and also accelerating them, imparting each of them with kinetic energy.
3 As a result of the energisation of the electrons (which have a much higher charge/mass ratio and so are accelerated to a higher velocity), further electron/positive-ion pairs may be created by collision with neutral atoms. These then undergo the same separating process creating an electron avalanche. Both positive and negative coronas rely on electron avalanches.
4 In processes which differ between positive and negative coronas, the energy of these plasma processes is converted into further initial electron dissociations to seed further avalanches.
5 An ion species created in this series of avalanches (which differs between positive and negative coronas) is attracted to the uncurved electrode, completing the circuit, and sustaining the current flow.
now we could use
Peeks law,
but I'm not to sure how'd that work around Mercury!
Could we fiddle it to fit a sphere in space?
mv is an irregularity factor to account for the condition of the wires. For smooth, polished wires, mv = 1. For roughened, dirty or weathered wires, 0.98 to 0.93, and for cables, 0.87 to 0.83.
Lets call the surface of Mercury on a planerty scale smooth, so mv=1
r is the radius of the wires
As we are not talking about wire but a sphere here and Murcuries mean radius is 2,439.7 ± 1.0 km or as we are really after the surface area of a sphere, at least Murcuries the r=7.48 × 107 km²
S is the distance between the wires
S=??? .i.e. we don't know the distance between the two objects here, so lets just make one up based on Terrestrial positive
lightning between the ionosphere and ground of 100km and so S=10000km nice round number!
δ is the air density factor. It is calculated by the equation:
Which in space would, I imagine be negligible, so δ=0
gv is the "visual critical" potential gradient, and is calculated by the equation:
as we are not in Earths atmosphere here I could assume the electric-constant would be close enough? So gv=ε0 or whatever it maybe at the surface of Murcury, but will start there.
Could we butcher the equation like that and get something useful out of it?
On the "look" of it (the Spider crater) and the description between a positive and negative corona discharge I'd posit a negative coronal discharge!
Negative coronas
Properties
A negative corona is manifested in a non-uniform corona, varying according to the surface features and irregularities of the curved conductor. It often appears as tufts of corona at sharp edges, the number of tufts altering with the strength of the field. The form of negative coronas is a result of its source of secondary avalanche electrons (see below). It appears a little larger than the corresponding positive corona, as electrons are allowed to drift out of the ionising region, and so the plasma continues some distance beyond it. The total number of electrons, and electron density is much greater than in the corresponding positive corona. However, they are of a predominantly lower energy, owing to being in a region of lower potential-gradient. Therefore, whilst for many reactions the increased electron density will increase the reaction rate, the lower energy of the electrons will mean that reactions which require a higher electron energy may take place at a lower rate.
Mechanism
Negative coronas are more complex than positive coronas in construction. As with positive coronas, the establishing of a corona begins with an exogenous ionisation event generating a primary electron, followed by an electron avalanche.
Electrons ionised from the neutral gas are not useful in sustaining the negative corona process by generating secondary electrons for further avalanches, as the general movement of electrons in a negative corona is outward from the curved electrode. For negative corona, instead, the dominant process generating secondary electrons is the photoelectric effect, from the surface of the electrode itself. The work-function of the electrons (the energy required to liberate the electrons from the surface) is considerably lower than the ionisation energy of air at standard temperatures and pressures, making it a more liberal source of secondary electrons under these conditions. Again, the source of energy for the electron-liberation is a high-energy photon from an atom within the plasma body relaxing after excitation from an earlier collision. The use of ionised neutral gas as a source of ionisation is further diminished in a negative corona by the high-concentration of positive ions clustering around the curved electrode.
Under other conditions, the collision of the positive species with the curved electrode can also cause electron liberation.
The difference, then, between positive and negative coronas, in the matter of the generation of secondary electron avalanches, is that in a positive corona they are generated by the gas surrounding the plasma region, the new secondary electrons travelling inward, whereas in a negative corona they are generated by the curved electrode itself, the new secondary electrons travelling outward.
A further feature of the structure of negative coronas is that as the electrons drift outwards, they encounter neutral molecules and, with electronegative molecules (such as oxygen and water vapour), combine to produce negative ions. These negative ions are then attracted to the positive uncurved electrode, completing the 'circuit'.
A negative corona can be divided into three radial areas, around the sharp electrode. In the inner area, high-energy electrons inelastically collide with neutral atoms and cause avalanches, whilst outer electrons (usually of a lower energy) combine with neutral atoms to produce negative ions. In the intermediate region, electrons combine to form negative ions, but typically have insufficient energy to cause avalanche ionisation, but remain part of a plasma owing to the different polarities of the species present, and the ability to partake in characteristic plasma reactions. In the outer region, only a flow of negative ions and, to a lesser and radially-decreasing extent, free electrons toward the positive electrode takes place. The inner two regions are known as the corona plasma. The inner region is an ionising plasma, the middle a non-ionising plasma. The outer region is known as the unipolar region.
So RC maybe correct in he's assumption of the formation taking place in two separate events! But he's timing may be off, it may not be cosmological time here, the "grabens"/rays/channels formed just before the dielectric strength was exceeded and an spark/arc formed which then formed the crater, time wise maybe only seconds, minutes or hours hell maybe even days passed before discharge was initiated!
Hope that's sciencey enough for our resident boffins, but without the hard data to plug into a highly dynamic process at this stage I'm not to sure if the maths is of much use!
Sol Invictus, Reality Check, tusenfem, Tim Thompson, Ben M, Perp student and others, which bit is hard to understand?