How do I send a confirmation email to the purchaser after they bought a ticket?

You can enable and set up the autoresponder email in your form to ensure that the users who have filled and submitted your form receive the email confirmation. In your case, when someone purchases the ticket through your form they will receive an email confirmation if the autoresponder email is set up inside your form. Please check out the link below for more details:

https://www.jotform.com/help/26-Setting-up-an-Autoresponder-Email

Do review and let us know if you have any further queries.