Poltergeist Arc

The Poltergeist Arc or the Poltergeist Incidents that occurs within the Toaru Kagaku Railgun sidestory. It focuses on the series of earthquakes that are happening all around Academy City, which are called Poltergeist. It is the second anime-introduced arc and is part of the Toaru Majutsu no Index canon. The arc reintroduces the Capacity Down, and the closure to Kiyama Harumi's quest to revive her students that was first introduced in the Level Upper Arc.

Background
Kiyama Harumi, the developer of the Level Upper has been released by the Heaven Canceler using his vast influence in the city; with his help, Kiyama Harumi was able to locate all her students that were experimented on by Kihara Gensei, and to create a cure for their comatose state. She discovered a way to treat them, though her efforts have a great cost, everytime her students would try to wake up from their comatose, they would cause an AIM Dispersion Field Resonance with each other, triggering a RSPK Syndrome occurence where ever Haruue Erii is, as she is the one who accidentally triggers the Poltergeist occurences, as she communicates telephatically with one of the comatose children, Edasaki Banri.

Sporadic earthquakes in Academy City
Since Haruue Erii knew that her friend, Edasaki Banri - is asking for her help, she searchers for her all around Academy City. Every time Kiyama Harumi would attempt to wake Banri and the other children, they would cause a AIM Dispersion Field Resonance, and at the same time Banri would try to contact Erii telephatically, triggering a Poltergeist-earthquake.

Because of her constant search for her in various locations in Academy City, the earthquakes appear at random. Below is the list of named areas that were affected by earthquakes, before the it's confirmation as a Poltergeist-related event.
 * District 7
 * Cypress Park
 * School Garden
 * District 19

Academy City's response
In a meeting between Judgment, Anti-Skill and Academy City's disaster response organization, MAR, it was revealed that it was caused by a RSPK Syndrome occurence, and not something that is related to supernatural phenomenon, as rumors are spreading around the populace of Academy City. Here, Judgment and Anti-Skill is tasked to stop the spread of rumors in Academy City and prevent mass hysteria from occuring, as to lessen collateral damage, while MAR responds to poltergeist-related occurences, and are deployed in crowded areas.

Poltergeist incidents continue
The next large-scale Poltergeist incident occured at the Fireworks Festival, where Misaka Mikoto, Shirai Kuroko, Saten Ruiko, Uiharu Kazari and Haruue Erii are attending. The earthquake caused massive damage, but no casualties were reported, due to the quick actions of MAR and it's leader Telestina.

Another Poltergeist incident occured on the next day in Nature Park, where Erii and Kazari are spending time together. The poltergeist occurence caused massive damage on the park, and several casualties, numbering in 72 people injured, with 8 people in critical condition. Many of the victims were rushed to the nearby 5th Emergency Treatment Center for medical care, including Kazari. Haruue Erii is transferred to the MAR Base Research Laboratory, under suspicion of causing the poltergeist incidents and for treatment.

Discovery of Kiyama Harumi's students
Misaka Mikoto investigates the abandoned Advanced Education Department, after Haruue Erii divulges her relation to one of Kiyama Harumi's students, Edasaki Banri. Here, she discovers that Kiyama Harumi is looking for data on the Crystallized Esper Essence, as she discovered that it is the key in reviving her students. She later tells to Mikoto that she is the one causing the poltergeist incidents, as she has discovered a way on waking them up with the assistance of the Heaven Canceler, and every time she tries to revive them, they cause a AIM Field Dispersion Field Resonance with Haruue Erii, causing a poltergeist incident.

Later, Telestina takes custody of the children, after folloing Misaka Mikoto. Despite her protests, Kiyama Harumi yields to their demands.

Telestina's deception
Kazari visits a dispirited Kiyama Harumi, and urges her to help Telestina in waking the children up. When they reached the MAR Base, they discover that Telestina is the granddaughter of Kihara Gensei, the instigator of the experiments on Kiyama Harumi's students and the creator of the Crystallized Esper Essence. After assaulting Kiyama Harumi, Kazari and Harumi are escorted out of the building.

After reporting of Telestina's true nature, Misaka Mikoto goes alone to confront Telestina, feeling guilty that she led her to the comatosed children. Despite her best efforts, Mikoto is defeated by Telestina in her mechanical body suit and with the help of Capacity Down, which she tells Mikoto that she invented it. After Telestina leaves her, Kongou Mitsuko (who was in the care of MAR, as she was a victim of the poltergeist incident) rescues her.

Child Error Rescue
Kazari discovers that Telestina plans to transfer the children to a private laboratory owned by Kihara Gensei, and also discovers that Kiyama Harumi is tailing them. With the insistence of Saten Ruiko, Mikoto apologizes for going alone, and later resolves to rescue the children with them. Judgment contacts Anti-Skill on Telestina's plans, and urges them to assist them.

They later intercept an attack on Kiyama Harumi and saves her, Shirai Kuroko and Kongou Mitsuko face-off against squads of MAR, while Mikoto rides with Konori Mii who is following Kiyama Harumi's car, where Kazari and Ruiko instructs her on the destination. They are later attacked by Telestina who now uses a large mechanical mobile suit; despite Telestina's effort, Mikoto is able to destroy her suit, with the help of Shirai Kuroko (she caught up with Konori Mii, who she rides with until she arrives near Mikoto's location) who teleports one of the suits parts to Mikoto, as she uses it as a much more powerful railgun.

They arrive in an abandoned propulsion laboratory, here - they discover that all the comatosed children and Haruue Erii are safe and sound. However, Telestina returns and activates Capacity Down, incapacitating Mikoto, Kuroko and Kazari; Ruiko who is unaffected by the device is hinted by Kazari to find the control room to destroy the sound system. After severely beating Harumi and Mikoto, Telestina reveals her plans on using the children for an experiment using the Crystallized Esper Essence, to attain the coveted level 6. She is however, aware of the dangers of destroying the city when she uses the crystal on the children, but is apathetic about it. Before she begins the experiment, Ruiko is successful in destroying Capacity Down. Allowing Mikoto to strike back, they duel with railguns and despite Telestina's facsimile on Mikoto's railgun, she is finally defeated by her.

Kiyama Harumi, uses the crystal to revive the children, and finally is able to hear their voices again in a tearful reunion. Harumi later thanks Mikoto, where the latter blushes and smiles.

Aftermath
Telestina is later treated for her injuries, and is later taken into custody, she is later reported to be uncooperative with the interrogations. Meanwhile, the Child Error's are taken into a medical facility for rehabilitation, after years of being bed-ridden; they later prepare a message on a blimp for Kiyama Harumi as her birthday present (at the suggestion of Misaka Mikoto). Kiyama Harumi later sees the blimp from her room, with the children saying "I love you" to her, making Harumi weep.

Trivia

 * Despite the fandoms accusations of the arc being anime-exclusive, it is later revealed to be canon to the Toaru Majutsu no Index universe when Haruue Erii is referenced in the Toaru Kagaku no Railgun manga.