You can EMP blast whole continents with it. It is thought that in case of an all our nuclear attack at high up detonation like that would happen early one to disable as many electronics and communication facilities of the enemy.
Then of course countries have been working on EMP hardening military tech.
For example https://en.wikipedia.org/wiki/Nuclear_electromagnetic_pulse says that:
if the Starfish Prime warhead had been detonated over the northern continental United States, the magnitude of the EMP would have been much larger (22 to 30 kV/m) because of the greater strength of the Earth's magnetic field over the United States,
Then the Soviets also "played" around with that too:
The monitored telephone line was divided into sub-lines of 40 to 80 kilometres (25 to 50 mi) in length, separated by repeaters. Each sub-line was protected by fuses and by gas-filled overvoltage protectors. The EMP from the 22 October (K-3) nuclear test (also known as Test 184) blew all of the fuses and fired all of the overvoltage protectors in all of the sub-lines.
Which, you know, kinda makes me giggle a little. We, the US, attacked space with a hydrogen bomb. The scientific world wasn't actually sure what effects this would have and we're like, "Hold my beer and watch this."
And then, we bombed space. That might actually be one of the most American things we've ever done.
"F*ck you, space! Being all spacey and stuff!" (At least that's what it sounds like in my imagination.)
"During the Trinity test, Enrico Fermi recalled Teller's idea of igniting the atmosphere. In an attempt to relieve some tension, he started taking bets on whether the test would destroy the world, or merely glass the State of New Mexico."
And it still doesn't really make a difference, on the grand scale of things.
Space would probably just go "That's cute" ..if it even noticed it.
Space is used to vastly more stronger forces – the kinds that create planets and destroy stars. Heck, there's probably more energy being flung around in Jupiter's storms every day if not every hour, than we could ever produce on Earth.
We could literally blow our planet apart (though even that may be nigh impossible) and it still wouldn't make much of a difference to our own solar system, let alone the galaxy around it.
I think we would be a happier species if we accepted our insignificance and tried to make the best of our infinitesimal corner in time and space, rather than having delusions of grandeur, trying to one-up and cower fellow insignificants with insignificant acts..
"When the bomb burst, people told of blackouts and strange electrical malfunctions, like garage doors opening and closing on their own."
The Soviet tests are interesting. They actually managed to burn down an entire electrical power station with the EMP from one of their bombs.
Edit: looking into it more, the destruction of the power station is uncertain. There was definitely a fire at the Karaganda power station, but there's only one vague reference to it being destroyed as a result. Interesting how a question like "did this entire power station burn down in the 1960s?" can remain unanswered today.
Establishing the destruction of that power station today would be extremely difficult, short of American spy photos, I'd wager.
I believe the reason for using air rather than fluid is heat dissipation. Normal fluid brakes would boil if subject to the heat and the fluid would break down. When air brakes get hot, the pressure just goes up.
Competition has a way of getting out of hand, no?
And Van Allen was quite possibly thrilled about the possibility of measuring his discover, from strength and shape to stability. (Good thing it is stable, otherwise people would keep probing it.)
Also, the atmosphere contains almost no hydrogen (except a little bit in the form of water vapor).
The second reaction is really unlikely, so the helium-2 almost always decays back into hydrogens. That means that pure hydrogen fuses extremely slowly. That works out in, for example, the Sun, where tremendous heat and pressure is maintained for billions of years. It doesn't work so well in a bomb which can only maintain fusion-level temperatures and pressures for tiny fraction of a second.
Thus, fusion bombs always use deuterium or tritium. Practical bomb designs typically don't use those directly (hydrogen is a pain to work with), but rather use lithium turns into deuterium or tritium in the neutron-rich environment of a detonating bomb.
But what does make a big difference is the air around the bomb---a nuclear explosion in space is way different from one in atmosphere. X-rays from the nuclear reaction heat surrounding air to many millions of degrees  and that's what causes (most of) the fireball you see. In space, the only matter available to make a fireball is the weapon's structure, probably only a few hundred kg, and that dissipates and cools rapidly. Nuclear-armed air intercept missiles were built in the nineteen-fifties and sixties that depended for effectiveness on being in air to generate the necessary blast effects to kill a bomber with relatively inaccurate aiming, but in space, a nuclear explosion almost needs be a contact hit to do much mechanical damage...discounting nuclear radiation effects, of course.
 Fahrenheit, Celsius, Kelvin...it makes no difference.
> Third, in the absence of the atmosphere, nuclear radiation will suffer no physical attenuation and the only degradation in intensity will arise from reduction with distance. As a result the range of significant dosages will be many times greater than is the case at sea level. With such weapons the lethal radii (from nuclear radiation) in space may be of the order of hundreds of miles.
Second, thermal radiation, as usually defined, also disappears.
There is no longer any air for the blast wave to heat and much
higher frequency radiation is emitted from the weapon itself.
The black magic of a hydrogen bomb is that it focuses the explosive energy of a fission bomb to ignite a fusion explosion. Doing so requires a very specific configuration; any hydrogen on the outside of the bomb, regardless of its concentration, would not reach the appropriate temperature/pressure to fuse.
XKCD 10,000: https://xkcd.com/1053/
Edit: now I'm puzzled why this is collecting downvotes. :-)
The fusion reaction requires an awful lot of energy to get going, so it basically uses a fission bomb as a detonator.
When the fusion fuel burns the resulting neutrons are used to fission the tamper of the secondary and it's this fission is the main energy source for most H-bomb designs.
Sometimes the "pusher" around the fusion fuel capsule is also made of fissile material which gets compressed, or imploded, just like a normal fission bomb core, but with much higher forces and so much greater efficiency and effectiveness.
Additionally, while Uranium-238 is not normally fissile it can be fissioned with high energy neutrons. The "problem" with U-238 is that the energy range of neutrons that induce fissions only partly overlaps with the natural energy range of neutrons produced by fission reactions. Meaning that on average a given neutron emitted by a U-238 fission will cause fewer than 1 additional fissions, so it can't self-sustain a neutron induced fission chain reaction (which, I guess, is a good thing, otherwise nuclear bombs would be nearly trivial to make). However, fusion reactions generate very high energy neutrons, essentially all of which can cause fission in U-238. For this reason many thermonuclear weapons have a natural or depleted Uranium casing. Fission in the casing typically doubles the yield of the weapon compared to the yield from the primary/secondary fission/fusion reactions.
All of this can be dialed to suit different desires for bomb production or yield. For example, the "Tsar Bomba" was a 100 megaton 3 stage thermonuclear warhead design, it was tested without a fissionable Uranium outer casing to avoid production of nearly 50 megatons worth of fission product fallout over the test site (which was in Russia), as a result it exploded at around 50 MT yield, almost all of which (97%) was from fusion reactions. On the other hand, you have a device like the W-88 which is an incredibly compact warhead carried on US SLBM submarines. It is a thermonuclear warhead but you could also look at it as a two stage fission-fission device with a heavily fusion boosted secondary, as most of the yield comes from fission in the secondary and the casing.
For comparison, the estimated pressure at the Earth's center  is around 360 gigaPascals, about 1/16,000 that of the W88 secondary compression.
edited to add W88 implosion pressure link
Not to mention there is no appreciable amount of hydrogen in the atmosphere anyway.
"I know! We'll make Polonium-filled spark plugs for people's cars!"
This will divert the asteroid. How much depends on the mass of the asteroid and the magnitude of the ablation push. The latter is complicated: bomb yield, distance, yield spectrum, asteroid material, etc. If the asteroid is quite fragile (think comet nucleus instead of metal or rocky asteroid), it might break into smaller pieces.
In any event, there's no need for intervening air to couple energy from a nuke detonation to an object in space.
“Outer space” is basically everything outside of some fuzzy demarcation line (often, specifically, the Kármán line) marking the “edge” of Earth's atmosphere.
Deep space refers to space far beyond the earth-moon system and generally earths gravity.
Interplanetary space is the space withing solar system. interstellar space is space between stars.
What else to say instead?
But seriously, I wonder what specifically about the side effects here would cause a garage door opener to not only open the door, but also consequently close it again. Perhaps it completed one full cycle as a result of the blast? Guess we'll never truly know.
So when they will arrive with who knows what intentions we know whom to blame.