The Earth's atmosphere is hit by high-speed plasma continuously, in the form of the solar wind. The incoming plasma will be deflected by the Earth's magnetic field, and generally enters close to the north or south magnetic poles, forming aurora. Here's a nice picture of some:
Solar wind particles generally have kinetic energies of about 1keV per nucleon, which is about 500km/s, or about 0.0015c.
Occasionally though, you get blobs of plasma ejected from the Sun in the form of Coronal Mass Ejections which can travel a little bit faster. The flare that caused the Carrington Event of 1859 travelled at nearly 2500kms, still a bit shy of 1% of lightspeed.
According to wikipedia,
Auroras were seen around the world, those in the northern hemisphere as far south as the Caribbean; those over the Rocky Mountains in the U.S. were so bright that the glow woke gold miners, who began preparing breakfast because they thought it was morning. People in the northeastern United States could read a newspaper by the aurora's light. The aurora was visible from the poles to low latitude areas such as south-central Mexico, Queensland, Cuba, Hawaii, southern Japan and China, and even at lower latitudes very close to the equator, such as in Colombia.
It might be possible to get CMEs which reach velocities of about 0.01c from the Sun. Our star is just too relaxed to generate a superflare, so bigger and brighter CMEs will only likely occur in other planetary systems with unfriendly suns whose local environments will be so hostile that planets around them might not even have atmospheres anymore, let alone any sort of complex surface life.
Sticking with more plausibly sized Solar CMEs... as the velocity of the incoming cloud of plasma increases, you'll get brighter and brighter aurora, visible closer and closer to the equator. Almost inevitably, XKCD has some useful information on the subject:
Note the scope of the plasma impact here: CMEs can be tens of millions of kilometres across, and require something the size of a sun to generate, and require the Earth to be relatively close to the sun. The blast expands and weakens rapidly. You won't be getting some giant superenergetic plasmoid trucking in from extrasolar space... by the time it got to us, it would be just too diffuse to do anything interesting. As mentioned elsewhere ad nauseam, plasma weapons are a silly idea.