The Ugly, the Bad, and the Good
I don't know what you mean by "radiation storm." I'm going to make an assumption ("the Bad"), but the phrase sounds more like Star Trek technobabble than an actual atronomical or meterological event. Therefore, if you find no value in my answer, then I strongly recommend you specifically describe what you mean by "radiation storm."
My assumption for a "radiation storm" is this: Somehow, a pinhole forms in the planet's magnetosphere, upsetting the Van Allen radiation belt, such that a small geographic area is bombarded by the Solar Wind and cosmic rays.
A "small geographic area" is probably the size of Kansas. But you can handwave this.
What would happen? Basically the same thing that happens in a microwave. You'd cook everything, probably sterilizing the ground. In a desert, you might melt the silicates, turning the surface into a thin layer of glass.
But, that might not be what you want. So, let's think about this a bit...
Radiation vs. Radioactive
Part of the problem here is the difference between radiation and radioactive. When a nuclear bomb goes off, most of what the world experiences is radiation, which passes through everything (leaving sunburns, cancer and death in its wake) but is thereafter gone.
Radioactive, on the other hand, is an adjective applied to particles (like plutonium) that are also spread by the explosion. Radioactive particles are spread like snow and last between hours and centuries depending on exactly what particle has been left behind.
As was pointed out to me months ago, radiation does not breed radiation. If it did, your microwaved food would become radioactive.
Therefore, the only way to leave radiation behind as a consequence of the "radiation storm" is for that storm to be comprised of radioactive particles, which is pretty much never what you get from outer space.
So, long story short, if you're trying to create temporary radioactive wastelands due to these "radiation storms," you need to provide a source of radioactive particles. The source must be regularly producing these particles or they will die out on their own. I could be wrong, but generally speaking, I don't think suns do this.
But, what if you have a binary star system: your orange star and a small pulsar. Pulsars in a binary system pull material (radioactive material) from the other star — but let's tilt the pulsar's axis such that the emission beams occasionally sweep some of that radioative material out into the orbital plane ... where it periodically meets up with your now defensless planet (because the Van Allen belts were designed to stop really light radiation, not really heavy radioactive particles).