There are a few realities I'd like to address before answering the question.
Wiping out an American city, much less the largest ones, requires either blast yields well beyond the capability of any terrorist organisation, or numbers of nuclear weapons that would make the terrorist organisation one of the largest nuclear powers on the planet. This is particularly true of major cities such as Atlanta, Houston, and LA, which are defined by their suburban sprawl.
The US and USSR encountered this problem early in the arms race. They were building larger and larger bombs in their show of force, but these became ever more impractical to deliver if ever called upon - to say nothing of the cost to maintain. They eventually realized that they could achieve the same level of destruction by detonating lots of small weapons in a tight pattern.
Compare one really large bomb on New York City (a B-83, 1.2 megatons, the largest single warhead in the US arsenal)...
Against the close detonation of seven smaller ones (W76s, each 100 kilotons, which can be delivered by a single, sub-launched Trident II missile)...
Whereas the one big bomb definitely does damage, the seven smaller bombs' overlapping shockwaves will do exponentially more damage across a larger area, thus more completely wiping out the city using 58% of the yield of the one bomb.
This is why while the largest bombs ever tested hit yields in the 10s of megatons (and some weapons were designed with theoretical yields of 100 megatons - 5,000 times more explosive than the bomb dropped on Hiroshima) the majority of weapons currently in the US and Russian nuclear arsenals are in the few hundreds of kilotons. They're cheaper to maintain, easier to deploy, and can be clustered to create more damage than a single, larger bomb.
The other issue is that in the maps above, the bombs were detonated at their optimal altitudes. Given that a terrorist organisation is unlikely to have ICBMs and nuclear submarines at its disposal, they're probably looking at a ground delivery, ie, a surface detonation, which requires even larger yields to achieve the same scale of damage as an airburst.
For example, it would take a 3.5 megaton nuclear weapon being detonated at the surface to replicate the damage of the 1.2 megaton airburst depicted in the first image. Neither the US nor USSR ever deployed such a large weapon outside of a test.
So either the terrorists need twenty extremely large bombs that, frankly, would be impossible to acquire and deploy without someone noticing, or many dozens of smaller ones to detonate simultaneously, making the terrorist organisation on par with nuclear states such as the UK, India, and Pakistan.
Okay, as long as we're all accepting of these realities, we'll move on to the hypothetical - with one correction.
The question asks about the 20 largest cities, but American cities are greater than their defined areas. The 20 largest cities, going strictly by their defined city limits, are as follows:
Notice anything missing? Washington, DC, perhaps prime-of-prime targets for any terrorist organisation with a nuke (or 20) to spare, is the 22nd largest city in the US on its own, and so not on the list. Also missing are major transportation and infrastructure centers such as Boston (24), Atlanta (40), and Seattle (21).
I mean, really, if they've gone through the trouble of getting a bunch of nukes into the US, passing on DC and Boston to take out El Paso and Indianapolis seems like one hell of a strategic blunder.
However, if we modify the question slightly to the 20 largest metropolitan areas' core cities, then our target list looks like this:
The loss of those cities would be far more devastating to the US than the first 20.
Okay, so to stay within realistic parameters, let's say that the nuclear weapons come from Pakistan as the result of a particularly effective Taliban offensive. Although the world raises serious concerns about the security of Pakistan's nuclear arsenal, in order to save face, the government of Pakistan says, "Nope, everything is fine. They didn't get close to our stockpiles."
Meanwhile, their intelligence service begins freaking out over the loss of 20 nuclear weapons, each with an estimate blast yield of 45 kilotons - enough power to turn most downtown centers into ash.
By keeping the rest of the world in the dark about the severity of the breach of their nuclear security, those who stole the weapons are given ample time to dismantle the warheads and move them out of the country during the chaos. Somehow, sometime later, they arrive in the US, are loaded onto moving vans, and sent to their targets.
By the time Pakistani officials are forced to admit that they lost control of some of their weapons, it's too late.
At 2 p.m. on the East Coast, the peak business hour, the terrorists detonate their weapons, killing over two-million people and injuring millions more from shrapnel and burns. Even though most of the cities' areas remain intact due to the low yields of the blasts, their downtowns have ceased to exist - and fires are ignited well across the metropolitan areas.
It only takes minutes for panic to set in among the survivors. The 120 million people - more than one in three Americans - who live in the affected metropolitan areas are now desperately trying to get anywhere else but the cities they call home.
Outside the targeted cities, panic sets in as news of the blasts floods the Internet and the surviving cable and television networks' broadcasts. People voluntarily evacuate other cities as rumors and fears of additional bombs spread.
In Washington, DC, there are more pressing concerns. The bomb was detonated at 16th and K St, NW, just a few blocks due north of the White House. Whatever little of the mansion the 50psi overpressure did not destroy, the intense thermal radiation has ignited. The President and Vice President are almost certainly dead.
At the other end of Pennsylvania Avenue, the Speaker of the House, second-in-line to the presidency, was in his office overlooking the National Mall. When the fireball rises over the ruins of downtown, he has no shielding from its full effect, suffering a mix of second and third degree burns on his exposed skin. Some loose papers in his office ignite, and wood surfaces scorch.
When the blast wave hits the Capitol Building, it is a mere 2 psi overpressure - not enough to knock down the marble, but plenty to turn its blast-facing windows into projectiles.
The moment the Speaker's security detail, who were sheltered in the halls of the Capitol, rush in to evacuate him, he is alive, but in critical condition. There is now a leadership crisis:
Under the Presidential Succession Act of 1947, the Speaker assumes the role of Acting President unless he "fails to qualify." Does his incapacity mean he fails to qualify for the role? "Fails to qualify" is specifically defined in the Act as regarding Constitutional eligibility criteria, and makes separate, specific reference to "inability" - but only to the President, Vice President, and President pro tempore of the Senate. "Disability" is also specifically mentioned separate from a failure to qualify, but again only applies to the President pro tempore of the Senate and successive Cabinet officials.
The President pro tempore of the Senate has survived (with minor injuries) and, on learning of the Speaker's condition, urges that he be sworn in as Acting President for the sake of providing leadership to a stricken nation - just as soon as they can find the Chief Justice of the Supreme Court to provide a favorable interpretation of the law.
At the Pentagon, across the river from the blast, America's military leadership has survived mostly unscathed. A few high-ranking officials whose offices faced the blast have sustained minor burns, and some have been blinded, but the building has survived. It is one of the very few headquarters of government that has escaped the DC blast that is still operational.
While they bring the Armed Forces to its highest state of readiness, there is almost no question in the minds of military leaders that Pakistan was effectively complicit in the attack by waiting so long to raise the alarm. To them, it is only a matter of time before they are ordered to retaliate with the full might of the United States; but as the law does not allow for the Secretary of Defense to take full control of the National Command Authority, they have to wait for an Acting President to be sworn in.
At the same time, leaders of the civil service who have not been killed in the attacks make their way to secondary and tertiary continuity of government sites, and await instructions from the surviving heads of their respective agencies. Many Cabinet officials and their deputies have been killed, putting the Federal government's agencies in the hands of people whose authority to make orders is in doubt.
Meanwhile, financial markets around the world begin to implode. The tremendous loss of financial capital and power through the destruction of New York, LA, and Chicago has sent confidence tumbling. While heads of state and militaries brace themselves for further attacks, heads of finance wonder aloud if the world's reserve currency has just lost its value. Global depression seems imminent.
In the hours after the attack, the 50 States call up their National Guards in an attempt to bring order to the chaos now spreading across the country. Health services have been overwhelmed with the injured, law enforcement spread thin, and cities and States outside of the targeted areas struggling to manage the displaced and panicked masses.
The country's transportation network has largely ground to a halt, as the interstates have been clogged with refugees, air traffic grounded, and major rail hubs rendered inoperable. Most of its busiest seaports, too, have been knocked out of commission, either through damage (in the case of seven of the nation's 10 busiest) or their workers fleeing in the mass exodus from America's urban centers.
In the days following the attack, the President pro tempore of the Senate is sworn in as Acting President, as the surviving Supreme Court justices determine that the Speaker's ongoing incapacity means he fails to qualify for office; but they made no ruling on what might happen if the Speaker recovers.
Quorums of both houses of Congress managed to escape Washington and, in playing very loose with the text of the Constitution, have granted themselves the authority to meet in sessions outside the destroyed capital.
It did not take long for the US to lay blame for the attack at the feet of Pakistan, due to their failure to cooperate with the international community in the hunt for the stolen nuclear weapons, and the military has begun planning its response. The US did not have trouble convincing its allies in NATO, ANZUS, and others, to supporting its declaration of war.
A nuclear strike has not been definitively ruled out, although Iran, Russia, and China all warn - with deep sympathies to the millions killed, of course - of consequences should the US launch a retaliatory nuclear strike. India is less strident in cautioning against a nuclear strike, but keeps a close eye on prevailing winds as it readies its own nuclear arsenal.
The US economy, however, has effectively collapsed. Consumer confidence is at lows not seen since the 1930s, and absenteeism is at all-time highs, leaving the surviving urban centers of America as ghost towns. To prevent a full economic free fall, trading and banking has been halted; but that leaves many without access to funds.
Millions of people, mostly from the densely populated Northeast Corridor between DC and Boston, are now suffering from the effects of radiation sickness, and hundreds of thousands of them are likely to die as medical services continue to be stretched.
International aid is mobilizing, but with most major air and seaports out of action, it will take weeks for significant relief to make its way to the tens of millions of displaced and terrified people who need it.
The military response, once it is organized, is brutal. Over international objections, the US destroyed several major urban centers, but the consequences major powers warned about did not materialize. The US and its allies quickly overwhelm Pakistan's armed forces, their dual mandate to remove the government and quell the Taliban insurgency; and in the latter case, the US forces are particularly harsh in executing on their mandate.
Months after the attack, and the US economy has begun to show signs of life. Many have made their way back to urban areas which have been declared safe, but others have begun to settle in other cities, creating boom towns in the upper Midwest, New England, and mid-South. However, the strength and longevity of America's economic recovery is in doubt as the global depression persists and there is very open talk of replacing the US Dollar with the Euro as the world's reserve currency, leaving its value at historic lows.
The US capital is relocated to Denver, due in part to the destruction of the nation's historical, alternate capitals, its distance from the attacked cities, and the area's high number of Federal employees and major Federal installations. The political chaos in the aftermath of the attack, and in the beginnings of investigations into how such an attack could have been possible, has angered an already government-resentful population. The early election results to replace those Members of Congress killed in and as a result of the attack have shown a rise of third-parties and extremists.
America survives, but it's been scarred and forever changed.
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