Inclusion Criteria:  Age between 18-75 years Alcohol use disorder according to DSM 5, moderate to mild according to ADS Residential stay for alcohol detoxofication  Exclusion Criteria:  Cognitive deficits defined by MoCA <25 (Montreal Cognitive Assessment) performed at least 7days after alcohol detoxification and after at least 12 hours after benzodiazepine cessation History of cerebral stroke DSM-5 substance use disorders other than nicotine and alcohol  Contraindication for rTMS :  Pregnancy History of epilepsy or seizure Cochlear implants Cardiac pacemaker or intracardiac lines, or metal in the body Clinical history of complicated withdrawal symptoms History of severe head trauma followed by loss of consciousness Actual major depressive episode, schizophrenia according to the MINI (Mini International Neuropsychiatric Interview) Breastfeeding women Actual or history of organic failure including cirrhosis Absence of health insurance; or patient with AME Legal protection (curatorship or tutorship) Deprive of freedom or security measure No adequate mastering of the French language or no ability to consent Major socio-economic problem: homelessness No written informed consent Participation in another interventional study  Secondary inclusion criteria (before randomization):  - Abnormal executive function defined as at least 3 impaired measurements among 19 measurements of 7 tests (Stroop test, Wisconsin test; Trail making test, verbal fluency, 6 elements, Brixton test, Dual task Baddeley test) from the Greffex battery. Each measure will be considered as impaired if it is below 1.65 SD. The procedure and the measurement are standardized. The neuropsychological evaluation will be performed at least seven days after alcohol detoxification and after at least 12 hours after benzodiazepine cessation.