On the Sun s Electric-Field

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1 On the Sun s Electic-Field D. E. Scott, Ph.D. (EE) Intoduction Most investigatos who ae sympathetic to the Electic Sun Model have come to agee that the Sun is a body that acts much like a esisto with a elatively high voltage acoss it. It also seves as the cental anode in a spheical plasma dischage. The cathode (gound) in this dischage is a vitual cathode a suface located at a lage distance fom the Sun, seveal times the distance of the outemost planets. The entie volume fom the Sun out to the cathode contains plasma. Thus the name sola plasmasphee is used to descibe it. The oute suface of this plasmasphee is called the heliopause and is pobably a plasma sheath eithe a single o double laye (DL) of electical chage. The action of the plasma inside the sola plasmasphee is akin to the classical electic plasma dischage seen in a Geissle Tube 1. In the laboatoy this is often in the fom of a simple glass cylinde with an anode (high voltage electode) at one end and a cathode (low o efeence voltage anode) at the othe. The tube is filled with low-pessue gas, a voltage is applied to the electodes, and an electic plasma dischage takes place inside the tube. This dischage can be in the dak mode, glow mode, o ac mode depending on seveal vaiables, most notably the value of the electic cuent density that exists within the main body of the plasma. The cylindical shape of the typical laboatoy plasma dischage tube is quite diffeent fom the spheical shape of the plasma suounding the Sun. One pupose of this pape is to investigate the analytic consequences of that spheical geomety. Assumptions The Sun is a body at a positive voltage. It continuously adiates (dissipates) some 4x1 6 W which is the poduct of its voltage, V, times the cuent, I, passing though it. Like any body in space, it also can cay an electical chage. Fo example the chage caied by Eath esults in an electic field of as much as 1V/m at its suface. 1. The Sun is not an isolated point chage within a vacuum. It is a body that exists suounded by a sea of plasma. So the application of classical (fee-space) electostatic analyses to the sola envionment is inappopiate.. The sola plasma is geneally quasi-neutal 3, which means that the numbe of fee electons and the numbe of positive ions within any easonably sized volume (1m 3 to 1km 3 ) ae equal. This is not to say that quasi-neutality is stictly adheed to in all egions within the sola plasmasphee. It clealy is not. Maxwell s equations can be used in limited and well-defined ways especially in those egions of non-quasi-neutality.

2 3. The sola plasma (as any plasma) is not an ideal, zeo-esistance entity. Howeve, plasma geneally cannot suppot high-valued electic fields. Typically, if a highvalued voltage dop is imposed between two points in plasma, a DL will fom somewhee between those points such that the geate pat of the applied voltage diffeence will occu within it. Because of this, only low-valued electic fields can and do exist within the sola plasmasphee (along with one o moe such DLs). The Sun s E-field To quantify the Sun s electic field, we apply Maxwell s equations to its inheently spheical geomety. One of those equations states: the divegence of the electic intensity, D E, at any point, is equal to the chage density,, at that point. The quantity is the pemittivity 4 of the medium. div E( ) ( ) (1) o E( ) ( ) () This can also be witten in integal fom as E ds Q (3) This means that the total electical flux emeging pependiculaly fom the suface suounding any closed volume is equal to the net electical chage enclosed within that volume. In othe wods, electic fields begin on positive chages and end on negative chages. A total chage, Q, within a spheical volume whose suface aea is S, will poduce an electic field extenal to S. Because the suface aea of a sphee is 4, we have fom (3) E4 RS Q (4) whee R S is the adius of the Sun s anode suface (the adius of the effective oute limit of the Sun s intenal electic chage). Q o E (5) 4 RS The value given by expession 5 is the stength of the Sun s outwadly diected (assuming Q epesents positive chage) electic field immediately above its suface. We know little o nothing about the stength of this field because we have no way of calculating o measuing the value of Q o E. In witing the above, we ae implying that the electic field vecto has no altitudinal (latitudinal) o azimuthal vaiation it is isotopic, being a function only of, the adial dimension. We ecognize, howeve, that this is almost cetainly not the case at high sola latitudes o along the pola axis extenal to the Sun s suface. What is the stength of the E-field at some point,, fathe out fom the suface? If the Sun s suoundings contain no net electical chage, then we can answe, similaly as in expession 5: Q E( ) (6) 4 But, is now the adius of an imaginay sphee that is lage than the Sun ( > R S ). The idea, of couse, is that this lage sphee still only contains the oiginal amount of chage,

3 Q, that is on the Sun. Expession 6 tells us that as long as thee is no additional net chage located outside of the Sun s suface, the stength of the electic field emanating fom it deceases invesely as the squae of the adial distance at which it is measued. This is the only esult acceptable to those who ignoe the possible existence of chage densities within the plasma that suounds the Sun. It epesents an ove-simplification and, as such, yields a esult that is geneally invalid. Fo example, suppose thee is a laye (spheical shell) of chage density beginning out at some distance, 1. One of Maxwell s equations (expessions 1 and ) identifies the E- field that would be poduced in any such case. The geneal expession fo divegence in spheical coodinates is D divd D D sin (7) sin sin whee D = εe. Assuming an isotopic spheical geomety (in which thee is no azimuthal o altitudinal vaiation) the last two tems on the ight have zeo value and so expession (7) simplifies to the odinay diffeential equation: 1 d E( ) ( ) (8) d By efeencing the stuctue of typical laboatoy plasma dischages 5, it is well-known that the fist laye above the anode suface, called the anode dak space (ADS), can contain eithe positive o negative chage. In eithe event, the chage density in this space is essentially a constant, ρ ADS. Thus, fo values of in that egion, we have 1 d E( ) ADS (9) d This is satisfied by ADS E( ) (1) 3 The E-field within any such laye is thus a amp function in distance, whose slope depends on the value (and algebaic sign) of ρ ADS. Within such a egion of unifomly dense positive space chage, the electic field stength will incease linealy. Within a egion of unifomly dense negative space chage, the electic field stength will decease linealy. Fom (8) we conclude that the Sun s E-field cannot be discontinuous in egions whee thee ae only finite chage densities. This enables us to plot the stength of the Sun s electic field in such egions. Above the anode dak space thee ae seveal diffeent chage shells (layes). All of these ae assumed to contain unifom positive, negative, o zeo valued chage densities and thus expession (1) is valid thee. We must emembe that is measued outwadly fom the Sun s cente. Matching beginning and end-point values of the E() functions obtained fom (8) is accomplished by adding suitable constants of integation to achieve these bounday values. In geneal, equation (8) is valid fo a vaiety of possibly non-unifom chage density distibutions within the sola plasma. In this expession, ρ() is the excess chage density. If the plasma is tuly quasi-neutal, then ρ() =. If thee ae moe positive ions 3

4 than electons in a given egion, then ρ() > thee. If thee ae moe electons than +ions, ρ() is a negative quantity (ρ() < ). Let us postulate seveal diffeent functions fo E() and detemine the ρ() function that will poduce each of them via expession (8). See the table below. A thid column in the table lists a voltage distibution function, V(), that is consistent with the electic field function listed in the fist column. By definition, the E-field is the negative of the voltage gadient. In an isotopic spheical geomety this is: V E, all fo > R S. (11) Given any E() function, we integate (11) to find each voltage pofile: E() ρ() V() 1 k E E k 3 E E E ln k 4 E E E k 5 E 3E E k Table 1. Coesponding electic-field, chage density, and voltage as functions of adial distance. The fist ow of functions is simply a special case of expession (6) whee Q = and theefoe E =. This is the case of an unchaged (non-electic) Sun whee the value of V is abitay (dependent on what efeence datum is chosen). The second ow indicates that, if thee is no extenal excess chage density, the electic field will follow an invese squae law. Rows #3 and #4 suggest that, if thee ae moe positive ions than electons in the atmosphee of the Sun, that the electic field will be stonge fathe out fom the Sun than in case #. In fact, in case #4, we see that an excess chage density that tapes off invesely as the fist powe of distance, will poduce a constant stength E-field (independent of distance). It is often the case in electical dischages that a somewhat highe density of positive chage is found nea the anode, so these cases (#3 and #4) ae of moe than just academic inteest. The fifth ow of functions is a estatement of expession 1. Conside that the heliopause (the oute edge of the sola plasmasphee) seves as the vitual cathode fo the oveall dischage. We often find an excess of seconday electons nea the cathode of a plasma dischage. Any non-zeo electic field must end on a shell of electons. Fo a long distance inside the heliopause, as we tavel outwad fom the Sun, the sola plasma has 4

5 been quasi-neutal. The excess chage density has been essentially zeo-valued. Theefoe, accoding to the functions in ow #, the E-field has been vaying invesely as the squae of adial distance. Suppose that the heliopause consists of a laye of electons whose density is a constant (negative value) fo some distance beyond its inne edge. This coesponds to the 5 th ow of functions with E being a negative constant. Thus the electic field in that egion would be negative and would incease apidly in stength with inceasing distance,. This inceasing negative E-field would epesent an inceasing inwad foce on any positively chaged paticles in that vicinity. The stength of the voltage dop coesponds to the obseved cathode dop which is often the stongest such change in the entie dischage. Implications fo the Safie Expeiment It may be difficult to get accuate estimates of the E-fields that ae poduced within a small laboatoy plasma dischage such as the Safie 6 poject. The esults shown in Table 1 (expanded if necessay) may be useful in estimating the value of those fields fom voltage vs. distance data obtained fom a Langmui pobe. Conclusions The application of Maxwell s equations to the coect spheical geomety of the Sun s envionment suggests a set of non-zeo-valued electic-fields that EU theoists have long felt existed, but have not, until now, descibed quantitatively. DES (Updated Mach 13.) 1 Available: Scott, D.E. Pime on Gas Dischages, Available: 3 We avoid the unqualified wod neutal in ode not to eoneously imply inet. Ionization of even a faction of the atoms in a given plasma makes it an extemely good conducto. 4 Hannes Alfvén noted that the pemittivity of plasma could be appoximated as being c 1 V MH whee ε is the pemittivity of fee space and V MH is the velocity of a hydomagnetic wave in that plasma. 5 Scott, D.E. ibid 6 A Real Wold Test of the Electic Sun, Available: 5

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