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Accelerator first appeared as an antagonist in Toaru Majutsu no Index series during the Sisters Arc. He is now a main protagonist, alongside Touma Kamijou for Science Side; after being defeated by Touma He is the most powerful psychic esper currently residing in Academy City. His psychic esper power is Vector Redirection and his given esper name is "Accelerator, (一方通行 Ippō Tsūkō, lit. "One-Way Road").

Accelerator appears as a skinny teenager and has pale skin, moppy white hair and red eyes. This is caused by his ability, as it blocks ultraviolet rays, thereby preventing his body from producing melanin. His ability also has an affect on his hormones, as he stated in the manga series it was because of his power he has "...this genderless body" but evidence is hinted and stated throughout the series he is a boy. His only example was he told Last Order he has a thin, girlish waist. He also seems to have an affinity for black and white-themed clothing. When he is enraged or excited (such as when fighting a strong or amusing opponent e.g Kamijou Touma in the Sisters Arc) he breaks into a wide grin and laughs, giving him an almost maniacal appearance.

Due to the potential of his ability, Accelerator has been targeted by assassins and researchers throughout his life. As a result, he believes only in power and trusts no one. While fighting, he invokes fear and has a sadistic tone. He willingly joins the SISTER experiment to gain a reputation as the most powerful and feared psychic so that no one would dare be foolish enough to challenge him and won't hesitate to kill any who get in his way. The Sisters' memories of his behavior during the experiment may suggest that he is, in a way, a pacifist; because his power won't disappear, the only way he sees an end to the fighting is to be so strong and sadistic that no one would dare to raise a finger against him. He even seems to attempt to frighten the Sisters out of fighting or otherwise encourage them to refuse their battles.

After meeting Last Order, he strives to protect her (although he states he does not like her company, he tolerates her). He saved her from Amai Ao's plot and from being pursued from the Hound Dogs. He treats Index in a similar fashion, such as when he buys her lunch while searching for Last Order and by protecting her from the Hound Dogs. He has mellowed out to the point that he actually lectures a child in order to prevent him from getting himself killed after a hostage situation.

Much of his past is unknown, but Accelerator mentions that he once had a "normal name" which has yet to be revealed. The novels state that his last name consists of two kanji and his first name three. Accelerator as a child couldn't fit in with the other children due to his powers, harming those that tried to get close to him. Despite what bullies, adults, or city security tried, they were powerless against his vector changing ability. This has made him something of a loner and distrustful towards other people. After some time, Accelerator was discovered by Kihara Amata, who trained him in how to control his powers and influenced him enough for Accelerator to adopt his personality.

Accelerator's ability made him the subject of an experiment attempting to create the first Level 6 psychic; according to the city's best supercomputer, Tree Diagram, this feat could only be achieved by killing Misaka Mikoto, the 'Railgun', 128 times. However, because it was impossible to create 128 of these 'railguns', due to the 'Level 5 Mass Production Plan' only being capable of producing a sub-standard clone of Mikoto at a power of Level 2-3, a substitute plan was arranged where Accelerator would have to kill 20,000 Misaka clones in a variety of methods. He willingly joins the experiment to gain a reputation as the most powerful and feared psychic so that no one would be foolish enough to challenge him ever again. By the beginning of the Sisters Arc, Accelerator has already killed the first 10030 Misaka Clones and during the course of the arc, kills clone 10031 before the experiment is ultimately stopped.

After his defeat, he takes on a more heroic role, protecting a small girl named Last Order - a Misaka clone numbered 20, 001. Later he becomes weaker along with his powers due to Amai Ao shooting him in the head, damaging his brain. This forces him to use a cane and restricts the duration of his ability to only 15 minutes at a time, as well as causing him to lose more than half of his computation ability even with 10,000 SISTER's boosting his calculating ability. This time frame is eventually extended to 30 minutes after GROUP's support technicians modify it. His psychic esper powers are slowly recovering with the help of Heaven Canceler thanks to the Misaka Network.

He is a member of GROUP when he was forced to join by Etzali, after hearing how it was the best way for him to protect Last Order. As the most powerful esper of Academy City, his existence and powers are tied to the plans of Aleister Crowley, the founder of Academy City, along with Kamijou Touma. His greatest rival in the series is considered to be Touma. Accelerator and Touma are counterparts; one being the strongest and the other the weakest levels of espers respectively. Accelerator's greatest nemesis, however, is fellow Level 5 esper, Kakine Teitoku. Their battle allow both of them to discover their "Awakenening" esper states, which sees Accelerator defeat Kakine without the use of the Misaka Network to perform calculations for him. Accelerator briefly entered his awakened state when he killed Kihara Amata in the Academy City Invasion Arc.

Accelerator's ability creates a thin field of AIM around him, which allows him to modify the vector values of anything he touches. He is shown to be far stronger than any other Level 5 in Academy City, being able to easily defeat the "Awakened" #2 Level 5 esper Kakine Teitoku without awakening himself. It should be noted that this fight took place after Accelerator's brain was damaged and he was forced to start relying on the Misaka Network to do his calculations, which reduced him to having less than half of his former calculation abilities for Redirection. He can change the vector values of anything by touch; for example, he kills a Sister clone by reversing the flow of blood inside her body after putting his finger inside her wound. Furthermore, this ability is automatic, so projectiles like bullets or explosives have no effect on him, as they will be redirected. It is because of his ability that he has an albino appearance, as his body blocks all unnecessary ultraviolet radiation, thereby preventing the skin from manufacturing unnecessary melanin. Thus far, he has shown the following ways to use his powers:
- Earth Stomp: Using the vectors behind his feet, he causes a little explosion made of earth and rocks to attack his opponents.
- Vector Shooting: By touching an object, he can extend the influence of his ability to other objects in contact with it.
- Wind Control: He can re-vector the surrounding winds and force them to congregate at a single point creating an extremely high velocity wind.
- Plasma Storm: He can even create plasma by further compressing the wind at high speeds in a single point.
- Kinetic Blast: Accelerator takes control of the planet's rotational vectors and transfers an enormous amount of that energy into one attack.
- Brain Hacking: By redirecting the electrical signals of the human body he can take 'control' over them and rewrite the memories and personality of the people as showed with Last Order.
- Flight: By controlling the wind around him he creates about 4 high-powered tornadoes behind him to allow him to fly.
- Reverse Engineering: Accelerator has stated that as long as he has experienced it, he can analyze forces unknown to him as long as his body has been in contact with it, by following the vectors that have been applied.
Along with his Vector Redirection ability, Accelerator also has his "Awakened" state.

He awakens towards the end of during the invasion of Academic City when he had a epiphany right before he was nearly killed by Kihara, and fully awakened in his fight with the other "Awakened" level 5, Kakine Teitoku during the Battle Royale Arc, which he displayed a massive difference in power between them. When he Awakens, Accelerator usually loses almost all conscious control of himself and begins to speak in the language of the Angels. He gains the ability to control and create "imaginary vectors", and no longer needs to be touching vectors to control them. When Awakened, he manifests massive black wings, stated to be made of the same "Dark Matter" that the #2 Level 5 Kakine Teitoku creates with his ability. These wings do all the vector-related calculations for him, and as a result he does not need the Misaka Network to manipulate vectors and "imaginary vectors" in his awakened form.

During the World War (World War III) Accelerator is currently in Russia, where he has a brief encounter with some Russian mages, and some of Academy city's new streamlined, high-speed power suits. It is also during this encounter where we learn that his ability not only works on magic (although incompletely, as the magic is dissipated instead of redirected) but also on teleportation as well. Accelerator also has an encounter with one of the new Level 4 Misaka clones, dubbed Misaka WORST, where he learns of Crowley's plans to make a new network with the new line of clones, and eliminate Last Order who has now become obsolete.

To save Last Order, he and Misaka WORST analyzed Index's song, that was stored on the Misaka Network, using his vector abilities to understand it and perform the spell. He was severely damaged by it, but completely cured Last Order. He is being transported back to Academy City after the war.