We report on event structure and double helicity asymmetry ($A_LL$) of jet production in longitudinally polarized p+p collisions at $sqrt{s}$=200 GeV. Photons and charged particles were measured at midrapidity $|eta| < 0.35$ with the requirement of a high-momentum ($>2$ GeV/$c$) photon in each event. Measured event structure is compared with {sc pythia} and {sc geant} simulations. The shape of jets and the underlying event were well reproduced at this collision energy. For the measurement of jet $A_{LL}$, photons and charged particles were clustered with a seed-cone algorithm to obtain the cluster $p_T$ sum ($p_T^{rm reco}$). The effect of detector response and the underlying events on $p_T^{rm reco}$ was evaluated with the simulation. The production rate of reconstructed jets is satisfactorily reproduced with the NLO pQCD jet production cross section. For $4 < p_T^{rm reco} < 12$ GeV/$c$ with an average beam polarization of $< P > = 49%$ we measured $A_{LL} = -0.0014 pm 0.0037^{rm stat}$ at the lowest $p_T^{rm reco}$ bin (4-5 GeV/$c$) and $-0.0181 pm 0.0282^{rm stat}$ at the highest $p_T^{rm reco}$ bin (10-12 GeV/$c$) with a beam polarization scale error of 9.4% and a $pT$ scale error of 10%. Jets in the measured $p_T^{rm reco}$ range arise primarily from hard-scattered gluons with momentum fraction $0.02 < x < 0.3$ according to {sc pythia}. The measured $A_{LL}$ is compared with predictions that assume various $Delta G(x)$ distributions based on the GRSV parameterization. The present result imposes the limit $-1.1 < int_{0.02}^{0.3}dx Delta G(x, mu^2 = 1 {rm GeV}^2) < 0.4$ at 95% confidence level or $int_{0.02}^{0.3}dx Delta G(x, mu^2 = 1 {rm GeV}^2) < 0.5$ at 99% confidence level.
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