This should be possible using the notification scheme of your Service Desk project.
Simply add the reporter to the notifications of an issue created.
You'll need to keep in mind that a user can indicate in his/her profile that they don't want to be notified of their own changes. If this is set they will not receive an email for an issue they created themselves.
In a hosted JIRA you would be able to solve this using the script runner plugin, but that plugin isn't available for OnDemand.
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