What is the burden of proving that a search warrant was issued on less than probable cause?

Normally, the issuance of a warrant by a neutral magistrate, which depends on a finding of probable cause, creates a presumption that it was objectively reasonable for the officers to believe that there was probable cause, see United States v. Ventresca, 380 U.S. 102, 109, 85 S.Ct. 741, 746, 13 L.Ed.2d 684 (1965), and a plaintiff who argues that a warrant was issued on less than probable cause faces a heavy burden, see, e.g., Rivera v. United States, 928 F.2d 592, 602 (2d Cir.1991) (search warrant). In order to mount such a challenge, the plaintiff must make a "substantial preliminary showing" that the affiant knowingly and intentionally, or with reckless disregard for the truth, made a false statement in his affidavit and that the allegedly false statement was "necessary to the finding of probable cause." Franks

Page 871