Date: 201702
Local time of day: 1201-1800
Location: ZZZ.Airport, US
Flight conditions: Marginal
Light: Daylight
Aircraft: A319
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Mission: Passenger
Flight phase: Takeoff / Launch
ATC / advisory: Tower ZZZ
Aircraft component: Turbine Engine
Component problem: Malfunctioning
Reporter organization: Air Carrier
Reporter function: Captain; Pilot Not Flying
Reporter qualification: Flight Crew Air Transport Pilot (ATP)
Second reporter function: Pilot Flying; First Officer
Anomaly: Aircraft Equipment Problem Less Severe; Flight Deck / Cabin / Aircraft Event Illness / Injury
Detector: Person Flight Crew
When detected: In-flight
Result: Flight Crew Rejected Takeoff
Contributing factors: Aircraft
Primary problem: Aircraft

Narrative: In 37+ years and 26000 hours of jet multi engine flight experience this report involves a first for me. After a runway line up; I transferred aircraft control and assumed pilot monitoring duties. The PF stood the Thrust Levers up and as I went down the engine instrument columns and came back up I saw the engines accelerating in response to the thrust levers being advanced towards Flex Thrust. However; immediately after brake release and during engine spool up to Flex thrust; apparently an uneven engine spool up/asymmetrical thrust condition quickly developed that was pronounced enough to abruptly cause the aircraft nose to swerve left. I write 'apparently' because; as PIC; I immediately went heads up; assumed aircraft control; and simultaneously retarded both thrust levers to idle while quickly stopping the aircraft in order to stabilize it.  The aircraft was brought to a stop in 30 feet or less from brake release. I immediately questioned the pilot flying as to whether he had inadvertently applied left brake after brake release since the aircraft had swerved to the left. After confirming he did not; I suspected #1 engine had not completely spooled up before advancing the TLs to Flex. I accomplished a quick systems/steering check; then spooled up both engines again to stabilize at 50% (normal procedure); then cautiously advanced both thrust levers and confirmed both engines were spooling up equally before once again transferring aircraft control and continuing the takeoff. The takeoff was normal afterwards. Furthermore; as pilot monitoring I confirmed and observed an even Engine Spool-Up when Reverse Thrust was selected after landing. After blocking in; the No 1 FA informed me that while taxing to the gate after landing; a customer seated in 26F had informed the No 2 FA that she had been sleeping and bumped her head on the seatback in front of her during the sudden braking after brake release on takeoff. However; the customer informed the No 1 and/or No 2 FAs she did NOT wish to be seen by paramedics for medical evaluation. I personally talked with the customer (who was apparently accompanied by another customer seated beside her) and explained what had caused the situation and stressed the importance of being evaluated by paramedics before flying on her connecting flight. Before advancing the thrust levers to rated thrust; it is CRITICALLY important that BOTH PILOTS ensure BOTH ENGINES ARE STABILIZED in a spooled up condition! I think I will make it a habit to personally spool up the engines before transferring control from this point forward. This should help prevent future embarrassment or worse; especially during contaminated/slippery runway operations.


Second narrative: [Report narrative contained no additional information.]


Synopsis: A319 flight crew reported an asymmetrical thrust condition on engine spool up during takeoff; a quick abort; and then a normal takeoff.