Tesla
Tesla is the last name of Nikola Tesla, the greatest mad scientist of all time. Seriously, the dude hardly slept and never had a partner because he was too busy being awesome. It's not like he couldn't pull either, he was considered super handsome in his time; in an interview, Tesla stated he never pursued women because he put them on such a high pedestal he considered himself unworthy of them, then when society changed he said he didn't find women appealing anymore because in his eyes they'd traded their noblest qualities for freedom (he indirectly blamed feminism but didn't hate women).
He is probably most famous for his impressive feats of electromagnetism, up to and including Alternating Current that allowed for long-distance power transmission and making electricity so cheap that even the modern poor can't survive without it, and more iconically the Tesla Coils that shoot lightning which is just fuckawesome. For his contributions to the field, a unit of magnetic flux density was named after him. His apocryphal and alleged inventions have also captured popular imagination, like his earth-resonator and death ray, to the point that the FBI had all his notes and property impounded after his death and called in an MIT professor to sift through it. Sadly, the search turned up nothing, but lots of science fiction has been set in alternate universes where Tesla was really onto something, resulting in an aesthetic heavily focused on Tesla coils, spark gaps, and exposed lightning. Such settings (and some settings set in the distant future) slap the word "tesla" on a lot of their technologies, especially the ones that shoot lightning -- tesla guns, tesla engines, tesla reactors, beans tesla-style, you name it. In this respect, it is very similar to the term "gauss".
When used as a name, "Tesla" is capitalized. When used as a unit or adjective, "tesla" is usually lowercase (though the abbreviation for the SI unit is a capital "T").
Warhammer 40,000
For the fifth edition Codex: Necrons, Games Workshop decided that the Necrons' iconic weapon, the gauss flayer (and its bigger brothers, the blaster, cannon, heavy cannon, and flux arc), needed some nerfing. Being able to automatically wound any infantry target on a six and automatically deal a glancing hit to a vehicle on a six was too much. If the Necron rule development team knew that 6th edition would include "hull points" that would cause vehicles to be wrecked after a certain number of hits (regardless of the results of rolls on the damage table), that was probably also a factor. The gauss rule's auto-glance property was retained, and the anti-light infantry effectiveness was moved to the Necrons' new tesla weapons, horde-killing assault guns that fire off high-strength bolts of lightning that ground themselves on the enemy. Their gimmick is that each to-hit roll of six grants two additional automatic hits on the same unit. Like Gauss weapons only kinda insta-gib vehicles, these weapons only sometimes insta-gib infantry. It does however make Snap Firing (like at Flyers or from Stunned vehicles) a right pain for your enemy, doubly so if the weapon is twin-linked.
They are similiar to the Imperium's Arc guns, but more advance and filled with more esoteric bullshit.
Tesla Carbine
A Tesla Carbine is a form of Necron Tesla Weapon that unleashes a bolt of living viridian lightning that crackles from foe to foe after hitting its target, charring flesh and melting armor. Tesla bolts feed off the energy released by the destruction, and the lightning discharge becomes more furious with every fresh arc, moving as if it had a mind of its own. In some cases, these energetic projectiles have even been observed to crack ceramite and plasteel.
Somehow, the Imperium still remembers the name of Nikola Tesla, thus they named these weapons after him. A Tesla Carbine is the smallest form of Tesla Weapon, and its rifle size makes it easily portable.
A unit of Immortals or Tomb Blades can choose to use Tesla Carbines instead of Gauss blasters, sacrificing the Gauss rule and 4+ armor-piercing ability for the chance to land extra hits.
Tesla Cannon
The Tesla Carbine's Lascannon.
Like its smaller brethren, the Tesla Cannon is a form of Necron Tesla Weapon that unleashes a large bolt of living viridian lightning that crackles from foe to foe after hitting its target, charring flesh and melting armor. Tesla bolts feed off the energy released by the destruction, and the lightning discharge becomes more furious with every fresh arc, moving as if it had a mind of its own. In some cases, these energetic projectiles have even been observed to crack ceramite and plasteel.
A Tesla Cannon is a large Tesla Weapon that is like a Tesla Carbine with another point of strength and twice as many shots. It is found underneath a Annihilation Barges and Catacomb Command Barges operators' pedals and acts as a secondary weapon. Tesseract Arks are also able to mount two Tesla Cannons as secondary weapon systems for twice the rapey power.
Tesla Cannons are powerful weapons that are most effective against infantry squads and light vehicles.
Tesla Destructor
Like its smaller brethren, the Tesla Destructor is a form of Necron Tesla Weapon that unleashes a heavy blast of living viridian lightning that crackles from foe to foe after hitting its target, charring flesh and melting armor. Tesla bolts feed off the energy released by the destruction, and the lightning discharge becomes more furious with every fresh arc, moving as if it had a mind of its own. In some cases, these energetic projectiles have even been observed to crack ceramite and plasteel.
A Tesla Destructor is the largest known type of Tesla Weapon, and such is the shocking rapidity of its fire that the lightning unleashed is capable of leaping from target to target so quickly that they are unable to ground themselves. A single direct hit from a Tesla Destructor might incapacitate an entire squad, leaving a trail of smouldering carnage across a broad swathe of the battlefield behind them. Due to a Tesla Destructor's large size, it is most commonly found mounted on vehicular platforms
The Tesla Destructor is again, another point of strength and twice as many shots compared to the Tesla Cannon. The Annihilation Barge, Night Scythe, and Doom Scythe all mount a twin-linked set of them for vaporizing infantry blobs.
Tesla Sphere
A Tesla Sphere is a form of Necron Tesla Weapon that unleashes a bolt of living lightning that crackles from foe to foe after hitting its target, charring flesh and melting armour. A Tesla Sphere is an arcane Tesla Weapon only found mounted on Necron Obelisks.
Each Obelisk will be armed with four such weapons around its hull capable of defending it against anything that enters the airspace around the war machine. Tesla Spheres have an extremely high rate of fire, even more so than a Tesla Destructor, and possess a similar range and degree of power output per shot to most other large Tesla Weapons.
Tesla bolts feed off the energy released by the destruction, and the lightning discharge becomes more furious with every fresh arc, almost as if moving with a mind of its own.
Also as of the Skitarii Codex the Adeptus Mechanicus is confirmed to have Nikola Tesla's preserved skull which they occasionally carry into battle to shoot lightning out of.