The 3 x 3 grid shown above is to be used in two separate ways:
A) Add 9 different positive integers so that each row, each column and both diagonals have the same product.
B) Add nine different positive integers to the same grid so that each row, each column, and both diagonals have the same minimal product.
There are many variants and types of plasma instabilities on the Sun which play both major and minor roles in events ranging from X-class solar flares to coronal mass ejections and even filament ejection-displacement. In this post I look at a few of these.
Conveniently, many of these instabilities are defined in terms of specific velocities. One of the more important of these is known as the electron drift velocity v d :
v d = I/ n e
where I is the current, n the number density (per cubic meter, for example) and e the electron charge. Often v d is defined instead based on current density (J) where: J = I/A (current in amps flowing through a magnetic flux tube or channel of some cross-section area A)
So: v d = J / n e
In many other cases, where J, I are not so easily obtained, v d will be the electron drift velocity in a combined magnetic and gravitational field, i.e.:
v d = m e g s c / e B
where B is the magnetic induction, e the electronic charge (1.6 x 10-19 C) , g s = 273 ms -2 the gravitational acceleration on the Sun, c is the velocity of light (2.98 x 10 8 m/s) and m e the electron mass (9.1 x 10 -31 kg) .
In the case of the ion-acoustic instability, the threshold for its onset is when:
v d > 43 v s
that is, the drift velocity is at least 43 times the ion sound speed, where:
v s = Ö (kT/ m i)
where k is the Boltzmann constant (1.38 x 10 -23 J/K), T the (Kelvin) temperature and m i the ion mass (e.g. m i ~ 1.7 x 10 -27 kg).
Sen and White in a 1972 paper dealing with the role of the Hall effect in flares, showed that the two-stream instability is incepted when the drift velocity:
v d > v ith
where v ith is the ion-thermal velocity:
v ith = Ö (2kT/ m i)
(rms value = Ö 3(kT/ m i)
In two-stream instability, when an electron flow is suddenly injected into a plasma – say for a coronal loop – the particles’ (Maxwellian) velocity distribution acquires a “bump” on its "tail" (higher velocity end of the distribution), consistent with two streams- an unperturbed one ( f o) and perturbed one ( f b ) applicable to the electron beam (See diagram below ).
In the region where the slope is positive (df v /d v > 0) there is a greater number of faster i.e. than slower particles so a greater amount of energy is transferred from particles to associated (e.g. Alfven) waves. Since f eb contains more fast than slow particles a wave is excited, and there is inverse Landau damping such that plasma oscillations with vph (phase velocity) in the positive gradient region are unstable.
Resonant electrons (at v ph > w e / k) where w e is the electron plasma frequency, i.e.
w e = [ne e2/ me εo] ½
are the first to be affected by the local wave-particle interactions and have distributions altered by the wave electric field, E1, such that the total energy balance:
E1 (TOT) = ½ E1 w + ½ E1 k
referencing the wave and kinetic (particle) contributions respectively.
Thus, for E1(TOT) = const. then as the electron velocity decreases, the particle kinetic energy decreases and the wave energy density increases.
In Landau damping the exact opposite occurs, so the gradient df(v)/d v decreases, and with it the wave amplitude, while the particle kinetic energy increases- i.e. wave energy lost is fed to the particles (electrons) which gain energy.
Note also that the "plasma beam instability" is just the finite temperature analog for the two stream instability. In other words, if one has a "two stream instability" one de facto also has the beam instability.
Lastly, for the Buneman instability, the relevant condition is:
v d > v eth
where v eth is the electron thermal velocity:
v eth = Ö (2k T e/ m e)
where T e is the electron temperature and k the Boltzmann constant.
The rms (root mean square) value for v eth is Ö 3 (k T e/ m e)
The objective for much better solar flare predictions is to be able to interpret which of these instabilities is near onset for a given solar plasma condition. This is not easy by any means, and probably requires much better optical resolution than available at present. However, solar physicists will "truck on" using all the resources they have to effect the best forecasts of which they are capable.
See also:
A Closer Analytical Look At Two Stream Instability...
And:
“Companies are not just maintaining margins, not just passing on cost increases, they have used it as a cover to expand margins."
"He was president for four years, we didn't all explode, institutions held, the threatened Constitution maintained."
Didn't all explode? Well, fortunately no, as Generals Kelly and Mark Milley fortunately pulled the plugs on two major crises (with N. Korea, China) before he could hit the nuclear codes. Gen. Kelly, for his part, noted at the time that Trump "is the most damaged person I've ever known in my life."
Constitution maintained? By a freaking hair, and only because honorable people were in key positions like Secretaries of State - many of whom have now been replaced by MAGA-ites. Further, as reported in the NY Times, plans are already in place by Trump's cult. Noting:
"Unlike the chaotic and improvised challenge four years ago, the new drive includes a systematic search for any vulnerability in the nation’s patchwork election system.
Mr. Trump’s allies have followed a two-pronged approach:
restricting voting for partisan advantage ahead of Election Day and
short-circuiting the process of ratifying the winner afterward, if Mr. Trump
loses."
See e.g.
How News Outlets Like Fox and CNN Are Preparing for Election Day - The New York Times (nytimes.com)
The orange maggot was also responsible for nearly a quarter million more U.S. Covid deaths thanks to his slack approach to the vaccines and masking, and even once suggesting "injecting bleach."
Oh, and lest Pegs forget, this depraved traitor incited an attempted coup to overthrow an election while rousing his minions in the January 6, 2021 attack on the Capitol. There they wrought all kinds of havoc, injuring many Capitol police when they weren't defecating in the halls. And she wants this loser Turd back in office rather than Kamala? Maybe she needs to take note of the recent endorsement of Kamala Harris by more than 700 National Security officers and specialists. As they wrote in their spot-on letter:
"This election is a choice between serious leadership and a vengeful impulsiveness. A choice between democracy and authoritarianism. Vie President Harris defends America's ideals while former President Donald Trump endangers them.
We do not make such assessment lightly. We are trained to make sober, rational choices. That's how we know Vice President Harris would make an excellent Commander-in-Chief while former president Trump has proven he is not up to the job."
I suggest Peggy Noonan read that over several times before she next scratches her noggin about the false equivalent fantasy of "Awful" vs. "Empty." For it is Trump who is both, awful and empty. He's an empty vessel and senile crackpot that even The Wall Street Journal held to opprobrium after his "pets getting eaten" barking in the Sept. 10 debate. ('False Claim That Immigrants Are Eating Pets Stirs Chaos', WSJ, p. A3, Sept. 14-15)
Further, Noonan might wish to process that the 700+ security and military officials wrote that Harris “grasps the reality of American military deterrence, promising to preserve the American military’s status as the most ‘lethal’ force in the world”. Adding:
“The contrast with Mr Trump is clear: where Vice President Harris is prepared and strategic, he is impulsive and ill-informed,” the letter reads.
And further:
"Mr. Trump denigrates our great country and does not believe in the American ideal that our leaders should reflect the will of the people. Mr. Trump is the first president in American history to actively undermine the peaceful transfer of power, the bedrock of American democracy.”
Let us further note that this endorsement letter also comes on the heels of another endorsement earlier this month by a group of 10 retired top US military officials, including retired Gen Larry Ellis, condemning Trump’s comments disparaging members of the military. Recall the orange maggot opted not to honor those who died at the Battle of Belleau Wood in WWI, calling them suckers and losers. See:
Is Pegs ok with a swine like that? A Captain Bonespurs who got his daddy Fred to get him a Selective Service waiver without even having to take a draft physical (like I did).
Or maybe she's fine with Trump being a 34 -times -convicted felon. Maybe she somehow missed the horrendous plans in Project 2025:
Project 2025, Explained | American Civil Liberties Union (aclu.org)
Including the part of the plan that will allow a new Trump authoritarian dictatorship to monitor women's menstrual cycles to find a 'tell' giving them the basis to prosecute them for any attempt to get out of state abortions e.g.
by Maya Boddie | September 27, 2024 - 6:40am | permalink
Donald Trump's senior adviser Jason Miller says that under a second Trump presidency, "it's 'going to be up to the states' whether or not they set up regimes to monitor women’s pregnancies so they can prosecute them for getting out of state abortions."
During a Wednesday Newsmax interview, the conservative interviewer asked, "[Trump] wouldn't support monitoring pregnancies even if a state decided to do that?"
Miller replied, "Well, he's made it very clear that he's not gonna go and weigh in and try to push various states in how they want to go and set up their particular rules and restrictions. That's gonna be up to the states."
Conservative and Bulwark founder Charlie Sykes replied: "Oh."
Still time to restore some measure of journalistic honor, Peggy, but I only give you one more week to do so. That is, by writing a new column praising the 700-plus national security specialists for their endorsement, and now YOU also praising Kamala Harris as the only rational (and patriotic choice) to Donald Traitor Trump.
That will at least prove to me you have an IQ over 100 and also still believe this nation should not be the stomping ground of scoundrels, traitors, chronic liars and demagogues. I want you especially to take back in full the blarney you wrote: "Failing to speak plainly about illegal immigration is political malpractice" - when the rat-faced fungus Trump blew out wackadoodle tales of immigrants eating pets in Springfield, OH. Which even the purveyors (excepting JD Vance) have come clean and admitted were errors or lies. Such as the owner of the cat, Miss Sassy, who blamed neighbor immigrants for eating her pet, then found it later hiding in her basement. All of this B.S. setting off lockdowns, bomb threats and chaos. Because of two Repuke fucktards, Trump and Vance.
You owe it to yourself as a putatively honest scribe to come clean and ignore those who might attack you in the WSJ Letters section. As they did after your first (Sept. 14-15 column) which led the way to the absurd, fact- free later one giving a nod to Trump despite his monumental defects.
See Also:
Sam Elliott - Time to be a man and vote for a woman:
And:
And:
by Tom Engelhardt | September 28, 2024 - 5:43am | permalink
Imagine yourself in space, looking down on our world and yet unable to return any time soon.
Consider it our bad luck, in fact, that Barry “Butch” Wilmore and Sunita Williams were the two Americans sent to the International Space Station, 250 miles above this planet, for a few days in June and now find themselves stuck there until perhaps next February. If only it had been former U.S. President Donald Trump and running mate Sen. JD Vance (R-Ohio).
If only indeed.
Of course, in some sense, both of them are already in deep space, far beyond where Wilmore and Williams find themselves. And if you don’t believe me, just ask any dog or cat from Springfield, Ohio.
And:
by Thom Hartmann | October 1, 2024 - 5:57am | permalink
“Menstrual police?” you may be thinking. That’s not possible! Not in America!
Read on.
The Comstock Act is an 1873 law that, if enforced, would outlaw all abortions in America by banning the shipping via mail, UPS, FedEx, etc., of any device, drug, or instrument that can be used to produce an abortion. It would even shut down hospital abortions.
It could also be used to empower new state or even federal police agencies specifically overseeing women violating its provisions. Like the menstrual police, which a Trump senior advisor just said was a very real possibility.
And:
by David Badash | September 24, 2024 - 6:27am | permalink
Donald Trump was asked twice to share specifics on his economic plans, but offered none. Instead, the Republican presidential nominee who recently helped launch his family’s new cryptocurrency venture attacked his Democratic opponent and rambled about the Presidents of Russia and China, while vowing to cut the cost of energy without stating how that would happen.
In an interview that aired Sunday on the Sinclair network, which broadcasts under local affiliates of Fox News, ABC, CBS, and NBC, “Full Measure” host Sharyl Attkisson asked Trump: “What are the specific mechanics of how prices come down? You know, the steps that would be taken in a second term for you?”
Trump began his response by attacking Vice President Harris, saying, “first of all, she can’t do an interview. She could never do this interview because you ask questions like give me a specific answer. She talks about her lawn when she was growing up.”
He continued his attacks before going after President Joe Biden and former Presidents Barack Obama and George W. Bush, then moving on to oil and geopolitics.
And:
And:
And:
by David Badash | September 25, 2024 - 6:04am | permalink
Republican presidential and vice-presidential nominees Donald Trump and JD Vance are facing criminal charges and an arrest request related to their weeks-long false claims that Haitian immigrants are stealing the pets of Springfield, Ohio residents and eating them.
The nonprofit Haitian Bridge Alliance is utilizing an Ohio state law that allows private individuals to file criminal charges, Cleveland ABC affiliate News5 reports. Through its attorney, the group is asking a judge to validate the charges and issue arrest warrants.
“The Haitian community is suffering in fear because of Trump and Vance’s relentless, irresponsible, false alarms, and public services have been disrupted,” according to The Chandra Law Firm‘s lead counsel Subodh Chandra, a former federal prosecutor. “Trump and Vance must be held accountable to the rule of law. Anyone else who wreaked havoc the way they did would have been arrested by now.”
“There’s nothing special about Trump and Vance that entitles them to get away with what they’ve done and are doing. They think they’re above the law. They’re not.”
And:
by Harvey Wasserman | September 24, 2024 - 5:30am | permalink
Donald Trump’s “Vigilante” campaign to steal your vote could soon put him in the White House… and land you and Taylor Swift in prison.
Mainstream polls now show Kamala Harris slightly ahead in key states. Most indicate that if the election were held today, Harris/Walz would narrowly win.
But they miss a deadly reality:
Nationwide, Trump has deployed thousands of MAGA vigilantes to strip likely Harris voters from the registration rolls. Thus anti-Trump citizens whose poll numbers bolster Democratic hopes may never get the ballots they need to actually decide the election.
In Georgia, MAGA activists have already submitted mega-lists challenging voting rights of hundreds of thousands of suspected (mostly young and of color) Democrats. The challenges require citizens to appear in person at their local election boards to confirm their identity. There’s no legal requirement they be notified of their disenfranchisement. Those who do go to the election boards can be rejected at will by Pro-Trump plants.
In its most recent year-end letter, the private equity firm Blackstone gave its stockholders a seemingly counterintuitive assurance: the lack of new housing stock was reason for optimism.
Why does a stagnant growth in new living spaces benefit Blackstone? Because it is the nation’s largest corporate landlord. For the firm and its investors, chronic housing shortages mean more power to set prices and more leverage to extract wealth from vulnerable working-class tenants.
Blackstone’s letter reveals the malevolent and distortionary role private equity plays in our residential real estate market and underscores the fundamental problem with housing commodification writ large.
Our market-based system simply does not give the private sector incentives to meet the public’s demand for high-quality, permanently affordable housing. Providing it would be against the sector’s economic interests since new supply would bring down prices and negatively impact profitability.