Dr. Cap Jackson is a psychiatrist who specialized in treating people suffering from sex addiction, a disorder that he himself suffers from.
Background
Cap was addicted to both alcohol and sex, and would repeatedly cheat on his wife. His serial philandering eventually drove his wife to suicide. When his daughter Ann turned sixteen, she and Cap went to their house in Falmouth, Massachusetts, with Ann's friend Linda. The girls went skinny-dipping and Cap joined them after drinking. After Ann went back to the house, Cap and Linda had consensual sex on the dock. Ann, who had recently come out as a lesbian, was outraged that Cap had sex with Linda, her first love, and stopped speaking to her father. Cap, who had forgotten about his one-night stand with Linda, misunderstood why Ann stopped talking to him, and for 20 years thought he had raped his own daughter. Cap eventually achieved sobriety and got a job treating sex addicts. He wrote a book about his experiences, titled "Eros, Run Amok".
On SVU
When a rapist attacks Ann and her partner Debbie Shields, Cap rushes to the hospital to see her. Detective Stabler suspects that one of Cap's patients attacked Ann and Debbie, and tries to get him to surrender his patient list, but Cap refuses. Stabler and Dr. George Huang question Cap about Ann's childhood, and he confesses that he thinks he raped Ann. Later, Stabler goes undercover in Cap's group therapy. Cap is initially hesitant to assist Stabler, but decides to help him after he meets with Linda and learns what really happened in Falmouth. Cap and Stabler eventually find out that Cap's assistant, Dr. Brett Kincaid, is the rapist. They stop Kincaid from raping another of Cap's patients, but Cap's professional reputation suffers as a result; when his patients learn that he let an undercover police officer into the group, they discontinue their therapy. Cap is later seen attending to his daughter with Debbie in the hospital. (SVU: "Mask")
Ann later dies from her injuries and Cap is forced to close down his clinic. Dr. George Huang later helps him get some consulting work for the FBI. When Huang takes a leave of absence from SVU, Cap is called to help SVU with investigating the rape and murder of a young girl named Marnie Allen. He suggests that the killer is a woman, and was probably abused herself. When the detectives come to suspect Marnie's piano teacher, June Frye, Cap suggests asking June for permission to search her house. When June tries to kill herself during the search, Cap performs CPR on her, saving her life. He tries to get June to talk, but she refuses. Eventually, however, she tells him that her father sexually abused her, and that she raped and killed Marnie. It is later revealed, however, that June's and her half-sister Katie Cavanaugh were in fact molested by their mother, Elaine Frye Cavanaugh, and that Katie killed Marnie. Cap assures June that he he will treat both of them. (SVU: "Totem")