## Friday, December 31, 2021

### Solutions To Plasma Physics Problems For Radio Astronomy (3)

1) Evaluate the Alfven velocity for the solar photosphere given:

r  =  2.0  x  10 -4   kg  m-3

=  0.1  Webers  -2

And   m =  m o    the magnetic permeability in vacuo

Solution:

m =  m o   =  4p  x  10 -7  hm-1

The Alfven velocity:

v =    B o / Ö(mr)

v =

(0.1 Wb  -2) Ö(4p  x  10 -4  hm-1)(2.0  x  10 -4   kg  m-3)

v =  6.3 x  10 3  ms-1  =    6.3  km/ sec

2) Re-evaluate to estimate r for the solar corona at about 1 solar radius above the photosphere, if  v »   2.0  x  10 8   m s-1

Solution:

Use algebra to make r  the subject:

r  =   m o  2

Then, on substituting the values of parameters:

r  =   (0.1Wb  -2) (4p  x  10 -4  hm-1)(2.0  x  10 8 ms-1) 2

r  1.9  x  10 -13   kg  m-3

## Thursday, December 30, 2021

### As Covid Infections Soar The U.S. Faces A Serious Mental Health Crisis - If It Doesn't Get Its Act Together

Besieged medical team using triage in ICU

"No jabs! I wanna drive the libs crazy, and take Biden down!"

"As large parts of our population reject common-sense solutions to limiting the spread of COVID through the best means available, what sort of reality are these vaccine deniers living in? It appears to me to be a sort of reality that is fantasy. One reality is undeniable. Evolution waits for no living thing to adapt to changing circumstances that threaten one’s very existence. Evolution will prevail, and it doesn’t respect fantasy."  Denver Post Letter writer, 12/31

As a record number (over 277,000) one- day Covid cases were reported yesterday, it's become even more clear this country is unable - and likely unwilling- to do what is needed to combat a relentless biological foe: the Covid virus.   Many health experts have compared what we're going through now to a war, and in a real sense they are correct. The difference is in this war we are battling a non-human predator and contagion that is capable of adapting (via mutation) and neutralizing our every advance via our own missteps. (Or unforced, stupid errors.)

That the response of so many Americans (39 million still unvaccinated) still hasn't changed is a testament to our current inability to have a collective response to defeat Covid.  Much of this is owing to a malignant politicization, both to the virus itself ("just a hoax") and to any mitigation responses - whether masking up, lockdowns or social distancing.  Over the past two years I've written posts referencing a number of the culprits as well as their disinformation -  which has undermined a uniform, collective response - such as we'd expect in a real global ground and air war.  E.g.

Brane Space: Profile Of Another Covid Quack: Joseph A. Ladipo (Still Peddling Baloney Amidst The Worst National Response To Pandemic) (brane-space.blogspot.com)

And:

Brane Space: The Glorified Quacks Behind "Herd Immunity" And Why Their Great Barrington Declaration Is Nuts - As A New Covid Variant Emerges (brane-space.blogspot.com)

I've also repeatedly warned of the danger of these new Covid variants,  i.e.

Brane Space: The New Covid Variants And The Danger Posed By A Faster Virus Mutation Rate (brane-space.blogspot.com)

and how they arise by virtue of too many people refusing to follow mitigation protocols and most critically, getting vaccinated.  But the drumbeat of disinformation isn't just from proven quacks (like Scott Atlas, Joseph Ladipo)  but sports icons like Packer quarterback Aaron Rodgers, who once again spouted codswallop two days ago.  This was by way of asserting on the Pat McAffee show in Milwaukee that he “doesn’t see how this can be a pandemic of the unvaccinated. (CDC Director Rochelle P. Walensky this summer said the country was in "a pandemic of the unvaccinated" where case counts were rising in communities with low vaccination numbers.)

This despite the fact when the Delta variant became the dominant strain earlier this year the unvaccinated people were found to be five times more likely to be infected, 10 times more likely to be hospitalized and 14 times more likely to die than those unvaccinated.  But "critical thinker" Rodgers isn't buying it.  Nope. golden boy Rodgers would rather further bamboozle his listeners (including many Pack fans) with this twaddle:

What I don't understand is vaccinated people blaming nonvaccinated people because the vaccine that they took to avoid getting the virus didn't stop them from getting the virus,"

Adding he just:   “wants a healthy debate to hear both sides”.

What both sides, you impenetrable ignoramus?  There is only one side, the one of science, of epidemiology, not pseudo-science of quacks like Scott Atlas.  Rodgers, if he had one grain of sense, wouldn't embarrass himself with these public declarations of his ignorance.  That includes failing to grasp that this virus mutates and churns because the unvaccinated are the perfect repositories for it to do so.  They are willingly providing living test tubes for the virus to survive and thrive - and change!  This has allowed more rapid mutation into variants that can break through our vaccine protections - such as we have seen with omicron, e.g.

Locations of omicron mutations (blue) and base insertions/deletions (red)

I.e. to generate what we refer to as "breakthrough infections."  In other words it is the unvaccinated who are giving rise to these infections that break through our vaccines.  If any Covid variant turns out to be vaccine resistant it is the unvaccinated who will be to blame.   It is therefore outrageous that Rodgers and
others  (like Tucker Carlson) have continued to fuel vaccine hesitance and refusal - the very things that would help us to escape the pandemic and finally reach true freedom. Not a bogus freedom as the antivaxxers pretend to have -  just for "defiant" scofflaws lacking common sense -   but for the whole nation.

We've since learned there is a terrible mental, psychological cost to the unwillingness of so many to cooperate, driven as they are by Republican lies and even paying people not to get the vaccines, e.g.

From a recent WaPo piece,

## The pandemic has caused collective trauma. Many people are near a breaking point.

"Across the United States, an alarming number of people are lashing out in aggressive and often cruel ways in response to policies or behavior they dislike

And :

"mental health experts said it’s likely that the worldwide state of perpetual crisis has truly spurred more frequent instances of inappropriate and abusive behavior.

Which elicits a question I raised barely two years ago:

Could this nation, if it had to endure a 6 -year major global war like World War 2,  be able to do it?

I doubt it. How could it when we learn (ibid.) some of those behaviors appear to be "the result of living through a long-lasting public emergency with no clear endpoint."   But look, a global war - like World War II - can also be like living through a long -lasting public emergency as my folks often attested to.  It was "all hands on deck" for them and their generation.  Yes, they agree Tom Brokaw's "greatest generation" meme remains a bit overblown, but they did learn how to make personal sacrifices, as did every other American, for the national welfare.  There was a collective will to triumph against an implacable, ferocious human enemy (the Nazis & Japanese Empire) determined to enslave much of the world if it prevailed. We do not see this today from the nation as a whole. It is as if a part of the populace has been split off to ally itself with the virus.

During the long global war, did we see people crack up and blow a gasket every other day? No, we did not. They put on their big boy pants and sacrificed with getting much less gasoline than they desired, and nowhere near the meat, milk, eggs or other staples. They didn't piss and moan about losing their preci0us freedom to gobble more steaks or fried chicken. It was a damned war for god's sake!  You sucked it up and moved on!

As the omicron variant rages across the country (now with an RO of 10 according to UK Professor of Infectious Diseases Martin Hibberd), it is again unclear when the pandemic restrictions will end.  But so what?  It doesn't matter!  As Chris Hayes pointed out on ALL In last night, the restrictions are put into place to prevent massive inundation of ERs, and hospitals.  Which even a so-called "mild" variant can produce given: a) the term "mild" is relative (as are many flus) so ICUs can still be overwhelmed, and (b) Supplies are already being stretched to the limit to the point that meds needed to sedate patients on ventilators are in short supply. ('Another Christmas of Death and Distress in America's ICUs',  December 26, Denver Post. p. 5A)

It shouldn't take over -stressed nurses crying and pleading with Americans to get get their jabs and wise up.  It does require we all pull together as one nation, as a people and stop the whining, yelling and fighting - whether about masks, isolating in quarantine when asked to and getting the vaccine.  And there is no damned room for  anyone getting uppity and defiant - either on a plane, at a school board meeting, or a grocery.('As Omicron Spreads, Unvaccinated Remain Defiant', Denver Post, p. 6A, Dec. 26)

These defiant imps need to back off and think of the mental harm their vaccine, masking refusal and prolonging the pandemic is having on the mental state of too many.  According to the WaPo piece:

"For some people, this kind of catastrophe strains their coping resources and causes them to act in ways that they normally would not."

And:

"Nearly two years into a pandemic coexistent with several national crises, many Americans are profoundly tense. They’re snapping at each other more frequently, suffering from physical symptoms of stress and seeking methods of self-care. In the most extreme cases, they’re acting out their anger in public — bringing their internal struggles to bear on interactions with strangers, mental health experts said."

Give me a freakin' break!  As long as the pandemic lasts we have to tough it out and that means getting control of emotions instead of letting them run riot.  That means not blowing one's top when a health expert - such as appearing on CBS yesterday morning - advised parents to mask up their two year olds  (and older) for the common good (Given that pediatric hospitalizations have doubled in the past week).   But at the same time we need the virus enablers   to cease helping it prolong our misery.   This is especially given that if omicron has an R nought of 10.0 it means 100 percent vaccination to halt its spread, this compared with R0 = 7 for Delta and 2.5 for the 'alpha' variant.

If we are to get through the next year without a national psychotic meltdown we need to develop a tougher mindset, and vastly more resilience as well as more political intelligence: the ability not to swallow propaganda wholesale and spread it around.  Thereby destroying all the work we've done so far this year, and meanwhile filling up ICUs and forcing triage care at understaffed hospitals. We especially need the unvaccinated resisters to stop their folly for the good of all. If they don't, then their own freedoms will have to be curtailed, i.e. in favor of formal vaccine passports (i.e. a uniform federal vaccine passport system)  - the lack of which means NO theater, no cinemas, no going to restaurants or to sports venues.

A good, serious sign (Denver Post, ibid.) is that Dr. Fauci now appears to be in favor of such a measure given sweet persuasion doesn't seem to make a dent on the defiant anti-vaxxers.   Thus in his telling, "if more businesses and organizations demanded such passports then a lot of people are going to realize that it's so inconvenient not to be vaccinated they could as well go ahead and do it."

Well, let's hope it doesn't come to that, but from where I stand, i tlooks like it might.

Excerpt:

The recent surge in COVID infections is being distributed in an alarmingly discriminating fashion. Data shows that it is predominantly spreading in the parts of the country that voted for Donald Trump. This should not come as a surprise to anyone who has noticed how Trump and his right-wing propaganda machine have downplayed the risks and discouraged responsible behavior such as getting vaccinated and wearing masks. Even worse, they have actually been celebrating the suffering and loss of life.

A new study by NPR confirms that "Counties that went heavily for Donald Trump have seen much lower vaccination rates and much higher death rates from COVID." However, this isn't the first time that the pandemic has been observed stalking Trump's cult disciples. As far back as July there were reports of this grisly statistic that pointed to the reality that we are in the midst of a "Pandemic of Fox News."

What makes this all the more disturbing is that, despite its unambiguous culpability, Fox News has failed to alert its audience to the deadly path that the network has put them on.

And:

## Most evangelical objections to vaccines have nothing to do with Christianity

And:

by Thom Hartmann | December 4, 2021 - 8:24am | permalink

And:

by Amanda Marcotte | December 28, 2021 - 7:38am | permalink

— from Salon

Excerpt:

Naturally, the source of right-wing anger at Trump was over the one good thing he's done: telling his base that it's good for people to get vaccinated against COVID-19. A week before Christmas, he got booed at an event after saying the vaccine was good, mostly because he wanted to take credit for it. When Trumpist grifter Candace Owens interviewed him a few days later, Trump rejected her anti-vaccine stance and insisted, correctly, that "the vaccine works" because "people aren't dying when they take the vaccine."

Because of this, folks across MAGAland are panning Trump for what is actually a very mild pro-vaccine stance (he still opposes mandates). Their language is sometimes surprisingly forceful.

## Tuesday, December 28, 2021

### The Plasma Physics Of Radio Astronomy (3)

The previous entry (Part (2)) assumed the presence of a low density plasma in which collisions are not important.  In addition while a magnetic field (B) was present it was not variable in the sense of being mechanically moved or displaced.  In this post we consider a layer of a conducting medium with an applied magnetic field which is moved or displaced.  No incident waves are considered but rather the effect of the motion of the medium in generating a disturbance or a wave.  The waves produced by such motion are known as magnetohydrodynamic waves.

Consider a slab in a conducting fluid such as shown in the top diagram. which is ,moved with a velocity v in the y -direction.  The slab is taken to be infinite in extent  in the  + y direction.  A steady magnetic field  B o   is applied in the z direction. Since v is in the y direction and B  is in the z-direction we have from the relation:

E  =  v x B

That an electric field E  will be induced in the x -direction by the motion. (Refer to Part (1)) This field produces a current in the slab in the x direction which has its return paths through the medium above and below the slab. This current, in turn, produces forces which tend to impede the motion of the slab but which also imparts an acceleration to the fluid   above and below the slab in the y direction.  Hence, the original motion initiates motion of the fluid which propagates as a wave parallel to the magnetic field.  The applicable equations become:

i)  Ñ X H  =  J    +  D /  t

ii)      Ñ  XE   =   - B  /   t

iii)     J  s  ( E + v XB )

iv)  B  =   m H

v)  dv/ dt =   G  +   1/r     (J x B  -   Ñ p)

Here:  v = velocity of displacement   (m/s)

J  = current density    (amp  m-2  )

r  = mass density  (kg  m-3 )

G = parameter involving non - EM forces (kg  m-1  s-2 )

Equations (i) and (ii) are Maxwell's curl equations, while (iii) is a form of Ohm's law for plasma involving the current density.  The equation (iv) is known as a constitutive relation describing the medium  and (v) is a hydrodynamic equation with the dimensions of acceleration.

From the geometry,  J y  =  J z  so that:

E  =  Jz/s  -  vy  Bo

And:  E y   =  E z = 0

Then from eqns.  (ii)   and (iv):

E  x / x m ¶  H y / t

Introducing the expression for E x into the above we get:

(vi)    m  ¶  H y  t =   B [¶  v  z]  - 1 / s  [¶  J  z ]

Neglecting G from equation (v) we obtain:

(vii)    ¶  v  t = - ( 1 / r)  J z   B o

Note: We assume here that  Ñ p  (grad p) can have no component perpendicular to z.  Now, let  D /  t << J and   introduce eqn. (i) into the preceding equation to obtain:

(viii)   ¶  v  t =   B o  r (  ¶  H z)

Eliminating  v  between eqns.  (vi)  and (viii) we obtain a wave equation:

2H y  t2  =

B2m r  ( ¶ H2  z2 )  +  1ms ( ¶ H / t  z2 )

Note that for very large conductivity, s , the last term can be neglected.   The velocity of the wave is then given by the Alfven velocity:

v =    B o / Ö(mr)

Where v is the velocity of the wave in m s-1

is the magnetic flux density in webers m-2

m  is the permeability of the medium in henrys m-1

r  is the density of the medium in  kg  m-3

Suggested Problems:

1) Evaluate the Alfven velocity for the solar photosphere given:

=  2.0  x  10 -4   kg  m-3

=  0.1  Webers  m -2

And   m =  m o    the magnetic permeability in vacuo

2) Re-evaluate to estimate r for the solar corona at about 1 solar radius above the photosphere, if  v »   2.0  x  10 8   m s-1