Event Management - notify participant on receiption of payment or on cancellation
You can do this in one of the two ways 


When you edit a participant you get an option to send confirmation email. Ticking the checkbox and saving the form will send email to contact.





Other option is to send reminder for particular participant status. Navigate to Administer >> Communications >> Schedule Reminders. On Add reminder form select entity as either Event Name or Event type and then select Event Name/Event Type and then Participant status with other fields.





  Note: Make sure Schedule reminder schedule job is enabled if you
  sending it via schedule reminder. But i would prefer to use method 1
  as it is most convenient and easy.


HTH 

Pradeep